Single-Photon Sources Combine High Purity, Indistinguishability and Efficiency All Together

From left to right: Chao-Yang Lu, Jian-Wei Pan, Sven Höfling and Christian Schneider.

Authors: Chao-Yang Lu¹, Christian Schneider², Sven Höfling^1,2,3,  Jian-Wei Pan¹

Affiliation:
¹CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.
²Technische Physik, Physikalisches Institat and Wilhelm Conrad Rontgen-Center for Complex Material Systems, Universitat Wurzburg, Germany.
³SUPA, School of Physics and Astronomy, University of St. Andrews, UK.

One-sentence summary: A single-photon source has been demonstrated which, for the first time, combines the features of high efficiency and near-perfect levels of purity and indistinguishabilty, opening the way to scalable multi-photon experiments on a semiconductor chip.

Spontaneous parametric down conversion has served as an excellent workhorse for fundamental test of quantum mechanics, quantum teleportation and optical quantum computing [1]. In this nonlinear optics process, the emission of photon pairs is probabilistic (with a probability of p) and inevitably accompanied by higher-order emission events (on the order of p²), which strongly limit the scalability for optical quantum information processing. So far, up to eight-photon entanglement—created from four independent photon pairs—have been demonstrated [2].

Past 2Physics article by Chao-Yang Lu and/or Jian-Wei Pan :
March 22, 2015: "Quantum Teleportation of Multiple Properties of A Single Quantum Particle" by Chao-Yang Lu and Jian-Wei Pan
January 04, 2015: "Achieving 200 km of Measurement-device-independent Quantum Key Distribution with High Secure Key Rate" by Yan-Lin Tang, Hua-Lei Yin, Si-Jing Chen, Yang Liu, Wei-Jun Zhang, Xiao Jiang, Lu Zhang, Jian Wang, Li-Xing You, Jian-Yu Guan, Dong-Xu Yang, Zhen Wang, Hao Liang, Zhen Zhang, Nan Zhou, Xiongfeng Ma, Teng-Yun Chen, Qiang Zhang, Jian-Wei Pan
June 30, 2013: "Quantum Computer Runs The Most Practically Useful Quantum Algorithm" by Chao-Yang Lu and Jian-Wei Pan.

In an attempt to overcome this obstacle, increasing attention has turned to single quantum emitters, such as self-assembled semiconductor quantum dots (QD), trapped atoms or ions, single defects in diamond or monolayer, and single molecules. In the past two decades, although many previous proof-of-principle experiments have established photon antibunching — an unambiguous evidence for single-photon emission, a scalable extension to multiple photonic quantum bits remain elusive.

To be useful for multi-photon applications such as Boson sampling, a perfect single quantum emitters should fulfill the following wish list: (1) High quantum efficiency: The decay of excited states should predominantly result in an emitted photon. (2) Deterministic generation: Upon a pulsed excitation, the source should deterministically emit one photon in a push-button fashion. (3) High purity: The emission should have a vanishing multi-photon probability. (4) High indistinguishability: Individual photons emitted at different trials should be quantum mechanically identical to each other. (5) High collection efficiency: The radiated photons should be extracted with a high efficiency to a single spatial mode.

Past 2Physics article by Sven Höfling :
May 17, 2015: "A Current Out Of Fluctuations" by Pierre Pfeffer, Fabian Hartmann, Sven Höfling, Martin Kamp, Lukas Worschech.

Among the discovered single quantum emitters so far, QDs have the highest quantum efficiency in solid state and narrowest linewidth at cryogenic temperature, and thus are promising as deterministic single-photon emitters. However, despite the extensive efforts, simultaneously fulfilling all the five criteria in the wish list proved challenging. Most previous experiments either relied on non-resonant excitation of a QD-microcavity that degraded the photon purity and indistinguishability [3,4], or used resonant excitation of a QD in a planar cavity that limited the extraction efficiency [5].

Figure 1: (a) Scanning electron microscopy image of a typical QD micropillar. (b) Numerical simulation of the photon emission from the QD-micropillar. (c) The photons collected into the first lens per pulse versus single-photon purity versus pump power.

Recently, the USTC-Wurzburg joint team exploited s-shell pulsed resonant excitation of a Purcell-enhanced QD-micropillar to deterministically generate resonance fluorescence single photons [6] which for the first time combines all the features in the wish list. The experiments were performed on an InAs/GaAs QD embedded inside a 2.5 micron diameter micropillar cavity (see Fig.1a) with a quality factor of 6124 and a Purcell factor of 6.3. Great efforts are made to find a single perfect QD at a sweet point where at 7.8 K the QD is to spatially coupled and spectrally resonant to the micropillar. At pi pulse, we detect 3.7 million single photon counts per second. The overall system efficiency is 4.6%. After correcting for detection efficiency and optical loss, we estimate that 66% of the generated single photons are collected into the first objective lens. Figure 1c summarizes the combined performance of the efficiency and single-photon purity as a function of pump power. It should be noted that the high generation and extraction efficiency are obtained with little compromise of the single-photon purity (g²(0) ≤ 0.009).

The overall system efficiency 4.6% — the highest reported in QDs — can be improved using techniques such as orthogonal excitation and detection of RF, near-unity-efficiency superconducting nanowire single-photon detection, and antireflection coatings of the optical elements. At this stage already, the performance of the single-photon source is already about ten time brighter than the triggered single-photon source used in eight-photon entanglement, but requires a pump power that is 7 orders of magnitude lower.

Figure 2: Quantum interference between two single photons separated by ~13 ns where the photon polarization set at cross (a) and parallel (b). A zoom-in near the zero time delay is shown in (c).

Another crucial demand is that the photons should possess a high degree of indistinguishability. We note that the pulsed resonant excitation is more critically needed for QDs with large Purcell factors where the reduced radiative lifetime approaches the time jitter. The single photons' indistinguishability is tested using two-photon Hong-Ou-Mandel interference. Figure 2a and 2b show histograms of normalized two-photon counts for orthogonal and parallel polarization at an emission time separation of ~13 ns, respectively. An almost vanishing zero-delay peak is observed for two photons with identical polarization (see Fig. 2c for a zoom-in). We obtain a degrees of indistinguishability to be 0.978.

Such a single-photon source can be readily used to perform multi-photon experiments on a solid-state platform. Immediate applications include implementation of Boson sampling [7] — an intermediate quantum computation where it is estimated that with 20-30 single photons one can demonstrate complex tasks that is difficult for classical computers. In addition to the photonic applications, the high-efficiency fluorescence extraction would also allow a fast high-fidelity single-shot readout of single electron spins, and efficiently entangling distant QD spins.

References:
[1] Jian-Wei Pan, Zeng-Bing Chen, Chao-Yang Lu, Harald Weinfurter, Anton Zeilinger, Marek Żukowski, "Multi-photon entanglement and interferometry", Review of Modern Physics, 84, 777–838 (2012). Abstract.
[2] Xing-Can Yao, Tian-Xiong Wang, Ping Xu, He Lu, Ge-Sheng Pan, Xiao-Hui Bao, Cheng-Zhi Peng, Chao-Yang Lu, Yu-Ao Chen, Jian-Wei Pan, "Observation of eight-photon entanglement", Nature Photonics, 6, 225–228 (2012). Abstract.
[3] Charles Santori, David Fattal, Jelena Vučković, Glenn S. Solomon, Yoshihisa Yamamoto, "Indistinguishable photons from a single-photon device", Nature, 419, 594–597 (2002). Abstract.
[4] Stefan Strauf, Nick G. Stoltz, Matthew T. Rakher, Larry A. Coldren, Pierre M. Petroff, Dirk Bouwmeester, "High-frequency single-photon source with polarization control", Nature Photonics, 1, 704 (2007). Abstract.
[5] Yu-Ming He, Yu He, Yu-Jia Wei, Dian Wu, Mete Atatüre, Christian Schneider, Sven Höfling, Martin Kamp, Chao-Yang Lu, Jian-Wei Pan, "On-demand semiconductor single-photon source with near-unity indistinguishability", Nature Nanotechnology, 8, 213–217 (2013). Abstract.
[6] Xing Ding, Yu He, Z.-C. Duan, Niels Gregersen, M.-C. Chen, S. Unsleber, S. Maier, Christian Schneider, Martin Kamp, Sven Höfling, Chao-Yang Lu, Jian-Wei Pan, "On-Demand Single Photons with High Extraction Efficiency and Near-Unity Indistinguishability from a Resonantly Driven Quantum Dot in a Micropillar", Physical Review Letters, 116, 020401 (2016). Abstract.
[7] Scott Aaronson, Alex Arkhipov, The computational complexity of linear optics, Proceedings of the 43rd annual ACM symposium on Theory of computing, 2011, San Jose (ACM, New York, 2011), p. 333. Full Article.

Quantum Computer Runs The Most Practically Useful Quantum Algorithm

Chao-Yang Lu (left) and Jian-Wei Pan (right) 












Authors: Chao-Yang Lu and Jian-Wei Pan

Affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, China.

Over the past three decades, the promise of exponential speedup using quantum computing has spurred a world-wide interest in quantum information. To date, there are three most prominent quantum algorithms that can achieve this exponential speedup over classical computers. Historically, the first one is quantum simulation of complex systems proposed by Feynman in 1980s [1]. The second one is Shor’s algorithm (1994) for factoring large numbers [2] – a killer program to break the widely used RSA cryptographic codes.

Very recently, the third one came as a surprise. Harrow, Hassidim and Lloyd (2009) showed that quantum computers can offer an exponential speedup for solving systems of linear equations [3]. As the problem of solving linear equations is ubiquitous in virtually all areas of science and engineering (such as signal processing, economics, computer science, and physics), it would be fair to say that this might be the most practically useful quantum algorithm so far.

Fig.1: An optimized circuit with four qubits and four entangling gates for solving 2x2 systems of linear equations.

Demonstration of the powerful algorithms in a scalable quantum system has been considered as a milestone toward quantum computation. While the first two have been realized previously [4,5,6], the realization the new quantum algorithm had remained a challenge. Recently, we report the first demonstration of the quantum linear system algorithm, through testing the simplest meaningful instance: solving 2×2 linear equations on a photonic quantum computer [7], in parallel with Walther’s group who also presented results on arXiv [8]. To demonstrate the algorithm, we have implemented a quantum circuit (see Fig.1) with four quantum bits and four controlled logic gates, which is among the most sophisticated quantum circuit to date.

Fig.2: Experimental setup. It consists of (1) Qubit initialization, (2) Phase estimation, (3) R rotation, (4) Inverse phase estimation.

An illustration of our experimental set-up is shown in Fig.2. The four quantum bits are from four single photons generated using a nonlinear optical process called spontaneous parametric down-conversion (where a short, intense ultraviolet laser shines on a crystal and, with a tiny probability, an ultraviolet photon can split into two correlated infrared photons). The quantum information is encoded with the polarization of the single photons, which can be initialized and manipulated using wave plates, and readout using polarizers and single-photon detectors [9].

In the experiment, it is also necessary to implement four sets of photon-photon controlled logic gates – that is, the quantum state of a single photon controls that of another independent single photon. These gates are realized by optical networks consisting of polarizing beam splitters, half wave plates, Sagnac interferometer, and post-selection measurement.

Fig.3: Experimental results. For each input state, the experimentally measured (red bar) expectation values of the observables of the Pauli matrices are compared to the theoretically prediction (gray bar).

We have implemented the algorithm for various input vectors. We characterize the output by measuring the expectation values of the Pauli observables Z, X, and Y. Figure 3 shows both the ideal (gray bar) and experimentally obtained (red bar) expectation values for each observable. To compare how close our experimental results match ideal outcome, we compute the output state fidelities, which give 0.993(3), 0.825(13) and 0.836(16) for the three input vectors, respectively.

To solve more complicated linear and differential equations [10], we are trying to develop new techniques, including experimental manipulation of more photonic qubits, higher brightness multi-photon sources, and more efficient two-photon logic gates. So far, we have the ability to control up to eight individual single photons [11] and ten hyper-entangled quantum bits [12]. Creating a larger-scale circuit would involve more quantum bits. Two parallel pathways are being undertaken in our group. One is to climb up to ten-photon entanglement, and the other way is to exploit more degrees freedom of a single photon thus using it more efficiently. The near-future goal is to control 10 to 20 photonic quantum bits. The enhanced capability would allow us to test more complicated quantum algorithms.

References: 
[1] Richard P. Feynman, “Simulating physics with computers”. International Journal of Theoretical Physics, 21, 467 (1982). Abstract.
[2] P. Shor, “Algorithms for quantum computation: discrete logarithms and factoring” in Proc. 35th Annu. Symp. on the Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society Press, Los Alamitos, California, 1994), p. 124–134. Abstract.
[3] Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd, “Quantum algorithm for linear systems of equations”. Physical Review Letters, 
103, 150502 (2009). Abstract.
[4] Chao-Yang Lu, Daniel E. Browne, Tao Yang, and Jian-Wei Pan, “Demonstration of a compiled version of Shor’s quantum factoring algorithm using photonic qubits”. Physical Review Letters, 99, 250504 (2007). Abstract.
[5] B.P. Lanyon, T. Weinhold, N. Langford, M. Barbieri, D. James, A. Gilchrist, and A. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement”. Physical Review Letters, 99, 250505 (2007). Abstract.
[6] Chao-Yang Lu, Wei-Bo Gao, Otfried Gühne, Xiao-Qi Zhou, Zeng-Bing Chen, Jian-Wei Pan, “Demonstrating Anyonic Fractional Statistics with a Six-Qubit Quantum Simulator”. Physical Review Letters, 102, 030502 (2009). Abstract.
[7] X.-D. Cai, C. Weedbrook, Z.-E. Su, M.-C. Chen, Mile Gu, M.-J. Zhu, Li Li, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan, “Experimental Quantum Computing to Solve Systems of Linear Equations”. Physical Review Letters, 110, 230501 (2013). Abstract.
[8] Stefanie Barz, Ivan Kassal, Martin Ringbauer, Yannick Ole Lipp, Borivoje Dakic, Alán Aspuru-Guzik, Philip Walther, “Solving systems of linear equations on a quantum computer”. arXiv:1302.1210v1. Abstract.
[9] Jian-Wei Pan, Zeng-Bing Chen, Chao-Yang Lu, Harald Weinfurter, Anton Zeilinger, Marek Żukowski, “Multiphoton entanglement and interferometry”. Review of Modern Physics, 84, 777 (2012). Abstract.
[10] Dominic W. Berry, “Quantum algorithms for solving linear differential equations”. arXiv:1010.2745. Abstract.
[11] Xing-Can Yao, Tian-Xiong Wang, Ping Xu, He Lu, Ge-Sheng Pan, Xiao-Hui Bao, Cheng-Zhi Peng, Chao-Yang Lu, Yu-Ao Chen, Jian-Wei Pan, “Observation of eight-photon entanglement”. Nature Photonics, 6, 225. Abstract.
[12] Wei-Bo Gao, Chao-Yang Lu, Xing-Can Yao, Ping Xu, Otfried Gühne, Alexander Goebel, Yu-Ao Chen, Cheng-Zhi Peng, Zeng-Bing Chen, Jian-Wei Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state”. Nature Physics, 6, 331 - 335 (2010). Abstract.

Quantum Teleportation of Multiple Properties of A Single Quantum Particle

Jian-Wei Pan (left) and Chao-Yang Lu

Authors: Chao-Yang Lu, Jian-Wei Pan

Affiliation:
CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.

The science fiction dream of teleportation [1] is to transport an object by disintegrating in one place and reappearing intact in another distant location. If only classical information is of interest, or if the object could be fully characterized by classical information—which can in principle be precisely measured—the object can be perfectly reconstructed (copied) remotely from the measurement results. However, for microscopic quantum systems such as single electrons, atoms or molecules, their properties are described by quantum wave functions that can be in superposition states. Perfect measurement or cloning of the unknown quantum states is forbidden by the law of quantum mechanics.

In 1993, Bennett et al. [2] proposed a quantum teleportation scheme to get around this roadblock. Provided with a classical communication channel and shared entangled states as a quantum channel, quantum teleportation allows the transfer of arbitrary unknown quantum states from a sender to a spatially distant receiver, without actual transmission of the object itself. Quantum teleportation has attracted a lot of attention not only from the quantum physics community as a key element in long-distance quantum communication, distributed quantum networks and quantum computation, but also the general audience, probably because of its connection to the scientific fiction dream in Star Trek. An interesting question is frequently asked: “would it be possible in the future to teleport a large object, say a human?” Before attempting to seriously answer that question, let us take steps back, look at where we actually are and think about a much, much easier and fundamental question: have we teleported multiple, or all degrees of freedom (DOFs) that fully describe a single particle, thus truly teleporting it intact? The answer is NO.

Past 2Physics article by Chao-Yang Lu and/or Jian-Wei Pan :

January 04, 2015: "Achieving 200 km of Measurement-device-independent Quantum Key Distribution with High Secure Key Rate" by Yan-Lin Tang, Hua-Lei Yin, Si-Jing Chen, Yang Liu, Wei-Jun Zhang, Xiao Jiang, Lu Zhang, Jian Wang, Li-Xing You, Jian-Yu Guan, Dong-Xu Yang, Zhen Wang, Hao Liang, Zhen Zhang, Nan Zhou, Xiongfeng Ma, Teng-Yun Chen, Qiang Zhang, Jian-Wei Pan

June 30, 2013: "Quantum Computer Runs The Most Practically Useful Quantum Algorithm" by Chao-Yang Lu and Jian-Wei Pan.

Although extensive efforts have been undertaken in the experimental demonstrations of teleportation in various physical systems, including photons [3], atoms [4], ions [5], electrons [6], and superconducting circuits [7], all the previous experiments shared one fundamental limitation: the teleportation only transferred one degree of freedom (DOF). This is insufficient for complete teleportation of an object, which could naturally possess many DOFs. Even in the simplest case, for example, a single photon, the elementary quanta of electromagnetic radiation, has intrinsic properties including its frequency, momentum, polarization and orbital angular momentum. A hydrogen atom—the simplest atom—has principle quantum number, spin and orbital angular momentum of its electron and nuclear, and various couplings between these DOFs which can result in hybrid entangled quantum states.

Complete teleportation of an object would require all the information in various DOFs are transferred at a distance. Quantum teleportation is a linear operation applied to the quantum states, thus teleporting multiple DOFs should be possible in theory. Experimentally, however, it poses significant challenges in coherently controlling multiple quantum bits (qubits) and DOFs. Hyper-entangled states—simultaneous entanglement among multiple DOFs—are required as the nonlocal quantum channel for teleportation. Moreover, the teleportation also necessitates unambiguous discrimination of hyper-entangled Bell-like states from a total number of 4^N (N is the number of the DOFs). Bell-state measurements would normally require coherent interactions between independent qubits, which can become more difficult with multiple DOFs, as it is necessary to measure one DOF without disturbing another one. With linear operations only, previous theoretical work has suggested that it was impossible to discriminate the hyper-entangled states unambiguously.

We have taken a first step toward simultaneously teleporting multiple properties of a single quantum particle [8]. In the experiment, we teleport the composite quantum states of a single photon encoded in both the polarization—spin angular momentum (SAM) — and the orbital angular momentum (OAM). We prepare hyper-entangled states in both DOFs as the quantum channel for teleportation. By exploiting quantum non-demolition measurement, we overcome the conventional wisdom to unambiguously discriminate one hyper-entangled state out of the 16 possibilities. We verify the teleportation for both spin-orbit product states and entangled state of a single photon, and achieve an overall fidelity of 0.63 that well exceeds the classical limit.

Figure 1: Scheme for quantum teleportation of the spin-orbit composite states of a single photon. Alice wishes to teleport to Bob the quantum state of a single photon 1 encoded in both its SAM and OAM. To do so, Alice and Bob need to share a hyper-entangled photon pair 2-3. Alice then carries out an h-BSM assisted by teleportation-based QND measurement with an ancillary entangled photon pair.

Figure 1 illustrates our linear optical scheme for teleporting the spin-orbit composite state. The h-BSM is implemented in a step-by-step manner. First, the two photons, 1 and 2, are sent through a polarizing beam splitter (PBS). Secondly, the two single photons out of the PBS are superposed on a beam splitter (BS, see Fig.1a). Only the asymmetric Bell state will lead to a coincidence detection where there is one and only one photon in each output, whereas for the three other symmetric Bell state, the two input photons will coalesce to a single output mode. In total, these two steps would allow an unambiguous discrimination of the two hyper-entangled Bell states. To connect these two interferometers, we exploit quantum non-demolition (QND) measurement—seeing a single photon without destroying it and keeping its quantum information intact. Interestingly, quantum teleportation itself can be used for probabilistic QND detection. As shown in Fig.1 left inset, another pair of photons entangled in OAM is used as ancillary. The QND is a standard teleportation itself.

Figure 2: Experimental setup for teleporting multiple properties of a single photon. Passing a femtosecond pulsed laser through three type-I β-barium borate (BBO) crystals generates three photon pairs, engineered in different forms. The h-BSM for the photons 1 and 2 are performed in three steps: (1) SAM BSM; (2) QND measurement; (3) OAM BSM.

Figure 2 shows the experimental setup for the realization of quantum teleportation of the spin-orbit composite state of a single photon. We prepare five different initial states to be teleported (see Fig. 3 left inset), which can be grouped into three categories: product states of the two DoFs in the computational basis, products states of the two DoFs in the superposition basis, and a spin-orbit hybrid entangled state. To evaluate the performance of the teleportation, we measure the teleported state fidelity

defined as the overlap of the ideal teleported state (|φ >) and the measured density matrix. The teleportation fidelities for |φ >_A, |φ >_B, |φ >_C, |φ >_D and |φ >_E yield 0.68±0.04, 0.66±0.04, 0.62±0.04, 0.63±0.04, and 0.57±0.02, respectively. Despite these experimental noise, the measured fidelities of the five teleported states are all well beyond 0.40—the classical limit, defined as the optimal state estimation fidelity on a single copy of a two-qubit system. These results prove the successful realization of quantum teleportation of the spin-orbit composite state of a single photon. Furthermore, for the entangled state |φ >_E, we emphasize that the teleportation fidelity exceeds the threshold of 0.5 for proving the presence of entanglement, which demonstrates that the hybrid entanglement of different DoFs inside a quantum particle can preserve after the teleportation.

Figure 3: Experimental results for quantum teleportation of spin-orbit entanglement of a single photon. The fidelities are above the classical limit and entanglement limit.

Our methods can in principle be generalized to more DOFs, for instance, involving the photon’s momentum, time and frequency. The efficiency of teleportation can be enhanced by using more ancillary entangled photons, quantum encoding, embedded teleportation tricks, and high-efficiency single-photon detectors. The multi-DOF teleportation protocol is by no means limited to this system, but can also be applied to other quantum systems such as trapped electrons, atoms, and ions, which can be expected to be tested in the near future. Besides the fundamental interest, the developed methods in this work on the manipulation of quantum states of multiple DOFs will open up new possibility in quantum technologies.

References:
[1] Anton Zeilinger, "Quantum teleportation". Scientific American, 13, 34–43 (2003). Link.
[2] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, William K. Wootters, "Teleporting an unknown quantum state via dual classic and Einstein-Podolsky-Rosen channels". Physical Review Letters, 70, 1895–1899 (1993). Abstract.
[3] Dik Bouwmeester, Jian-Wei Pan, Klaus Mattle, Manfred Eibl, Harald Weinfurter, Anton Zeilinger, "Experimental quantum teleportation". Nature, 390, 575–579 (1997). Abstract.
[4] Xiao-Hui Bao, Xiao-Fan Xu, Che-Ming Li, Zhen-Sheng Yuan, Chao-Yang Lu, Jian-Wei Pan, "Quantum teleportation between remote atomic-ensemble quantum memories", Proceedings of the National Academy of Sciences of the USA, 109, 20347–20351 (2012). Abstract.
[5] M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, D. J. Wineland, "Deterministic quantum teleportation of atomic qubits". Nature, 429, 737–739 (2004). Abstract.
[6] W. Pfaff, B. J. Hensen, H. Bernien, S. B. van Dam, M. S. Blok, T. H. Taminiau, M. J. Tiggelman, R. N. Schouten, M. Markham, D. J. Twitchen, R. Hanson, "Unconditional quantum teleportation between distant solid-state quantum bits". Science, 345, 532–535 (2014). Abstract.
[7] L. Steffen, Y. Salathe, M. Oppliger, P. Kurpiers, M. Baur, C. Lang, C. Eichler, G. Puebla-Hellmann, A. Fedorov, A. Wallraff, "Deterministic quantum teleportation with feed-forward in a solid state system". Nature. 500, 319–322 (2013). Abstract.
[8] Xi-Lin Wang, Xin-Dong Cai, Zu-En Su, Ming-Cheng Chen, Dian Wu, Li Li, Nai-Le Liu, Chao-Yang Lu, Jian-Wei Pan, "Quantum teleportation of multiple degrees of freedom of a single photon". Nature, 518, 516-519 (2015). Abstract.

Solving Linear Equations on Scalable Superconducting Quantum Computing Chip

From left to right: Chao-Yang Lu, Jian-Wei Pan, Xiaobo Zhu, H. Wang, Ming-Cheng Chen

Authors: Ming-Cheng Chen¹, H. Wang², Xiaobo Zhu^1,3, Chao-Yang Lu¹, Jian-Wei Pan¹

Affiliation:
¹Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China,
²Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China,
³Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.

One-sentence summary:
Quantum solver of linear system is achieved on scalable superconducting quantum computing chip.

The most ambitious target of quantum computing is to provide both high-efficiency and useful quantum software for killer applications. After decades of intense research on quantum computing, several quantum algorithms are found to demonstrate speedup over their classical counterparts, such as quantum simulation of molecular or condensed system [1], Grover search on unstructured database [2], Shor's period finding to crack RSA cryptography [3], matrix inversion to solve linear systems [4] and sampling from a hard distribution [5, 6]. Among them, sampling from a hard distribution is the most radical example to show the pure quantum computing power beyond the reach of any modern conventional computer and achieve "quantum supremacy" in the near-term [7].

However, the high-efficiency quantum supremacy algorithms have not been found to have practical applications yet. And the Grover search and Shor's period finding algorithms are limited to specific applications. On the contrary, the linear equations quantum algorithm can be applied to almost all areas of science and engineering and recently it finds fascinating applications in data science as a basic subroutine, for instance, in quantum data fitting [8] and quantum support vector machine [9].

Matrix inversion quantum algorithm to solve linear systems [4] is proposed by Harrow, Hassidim and Lloyd (HHL) in 2009 to estimate some features of the solution with exponential speedup. The algorithm uses the celebrated quantum phase estimation technology to force the computation to work at the eigen-basis of system matrix and reduce the matrix inversion to simple eigenvalue reciprocal. A compiled version of the HHL algorithm was previously demonstrated with linear optics [10, 11] and liquid NMR [12] quantum computing platforms, however, both of which are considered not easily scalable to a large number of qubits. Recently, we report the new implementation of the HHL algorithm on solid superconducting quantum circuit system, which is deterministic and easy scalable to large scale.

We run a nontrivial instance of smallest 2×2 system on superconducting circuit chip with four X-shape transmon qubits [13] and tens of one- and two-qubit quantum gates. The chip was fabricated on a sapphire substrate and used aluminum material to define superconducting qubits, resonators and transmission lines. With careful calibration, the single-qubit rotating gates were estimated to be of 98% fidelity and two-qubit entangling gates were of above 95% fidelity. Figure 1 and Figure 2 illustrate the quantum chip and the working quantum circuits, respectively.

Fig. 1: False color photomicrograph of the superconducting quantum circuit for solving 2×2 linear equations. Shown are the four X-shape transmon qubits, marked from Q1 to Q4, and their corresponding readout resonators.

Fig. 2: (click on image to view with higher resolution) Compiled quantum circuits for solving 2×2 linear equations with four qubits. There are three subroutines and more than 15 gates as indicated.

The quantum solver was tested by 18 different input vectors and the corresponding output solution vectors were characterized using quantum state tomography. In our 2*2 instance, the output qubit was measured along X, Y and Z axes of the Bloch sphere, respectively. The estimated quantum state fidelities ranged from 84.0% to 92.3%. The collected data was further used to infer the quantum process matrix of the solver and yielded the process fidelity of 83.7%. Figure 3 and Figure 4 show the experimental quantum state fidelity distribution and the quantum process matrix, respectively.

Fig. 3: Experimental quantum state fidelity distribution of the output states corresponding to the 18 input states.

Fig. 4: The real parts of the experimental quantum process matrix (bars with color) and the ideal quantum process matrix (black frames). All imaginary components (data not shown) of quantum process are measured to be no higher than 0.015 in magnitude.

These experimental results indicate that our superconducting quantum linear solver for 2*2 system have successfully operated. To scale the solver for more complicated instance with high solution accuracy, further improvement of device design and fabrication to increase quantum bit coherent time and optimization of quantum control pulses to reduce the operating time and error rate are necessary. In superconducting quantum circuit platform, there have been vast efforts devoted to scale the circuit complexity and quality, which have extended the qubit coherent time 5~6 orders of magnitude [14] manipulated up to 10 qubits [15] in the past decades, and we can expect the continuous progress in next decade to reach a mature level.

References:
[1] I. M. Georgescu, S. Ashhab, Franco Nori, "Quantum simulation". Reviews of Modern Physics, 86, 153 (2014). Abstract.
[2] P. Shor, “Algorithms for quantum computation: discrete logarithms and factoring” in Proc. 35th Annu. Symp. on the Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society Press, Los Alamitos, California, 1994), p. 124–134. Abstract.
[3] Lov K. Grover, "A Fast Quantum Mechanical Algorithm for Database Search", Proceedings of 28th Annual ACM Symposium on Theory of Computing, pp. 212-219 (1996). Abstract.
[4]  Aram W. Harrow, Avinatan Hassidim, Seth Lloyd, “Quantum algorithm for linear systems of equations”. Physical Review Letters, 103, 150502 (2009). Abstract.
[5] A. P. Lund, Michael J. Bremner, T. C. Ralph, "Quantum sampling problems, BosonSampling and quantum supremacy." NPJ Quantum Information, 3:15 (2017). Abstract.
[6] Hui Wang, Yu He, Yu-Huai Li, Zu-En Su, Bo Li, He-Liang Huang, Xing Ding, Ming-Cheng Chen, Chang Liu, Jian Qin, Jin-Peng Li, Yu-Ming He, Christian Schneider, Martin Kamp, Cheng-Zhi Peng, Sven Höfling, Chao-Yang Lu, Jian-Wei Pan, "High-efficiency multiphoton boson sampling". Nature Photonics 11, 361 (2017). Abstract.
[7] John Preskill, "Quantum computing and the entanglement frontier". arXiv:1203.5813 (2012).
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[10] X.-D. Cai, C. Weedbrook, Z.-E. Su, M.-C. Chen, Mile Gu, M.-J. Zhu, Li Li, Nai-Le Liu, Chao-Yang Lu, Jian-Wei Pan, "Experimental quantum computing to solve systems of linear equations". Physical review letters 110, 230501 (2013). Abstract.
[11] Stefanie Barz, Ivan Kassal, Martin Ringbauer, Yannick Ole Lipp, Borivoje Dakić, Alán Aspuru-Guzik, Philip Walther, "A two-qubit photonic quantum processor and its application to solving systems of linear equations". Scientific reports 4, 6115 (2014). Abstract.
[12] Jian Pan, Yudong Cao, Xiwei Yao, Zhaokai Li, Chenyong Ju, Hongwei Chen, Xinhua Peng, Sabre Kais, Jiangfeng Du, "Experimental realization of quantum algorithm for solving linear systems of equations". Physical Review A 89, 022313 (2004). Abstract.
[13] Jens Koch, Terri M. Yu, Jay Gambetta, A. A. Houck, D. I. Schuster, J. Majer, Alexandre Blais, M. H. Devoret, S. M. Girvin, R. J. Schoelkopf, "Charge-insensitive qubit design derived from the Cooper pair box". Physical Review A 76, 042319 (2007). Abstract.
[14] M. H. Devoret, R. J. Schoelkopf1, "Superconducting circuits for quantum information: an outlook". Science, 339, 1169 (2013). Abstract.
[15] Chao Song, Kai Xu, Wuxin Liu, Chuiping Yang, Shi-Biao Zheng, Hui Deng, Qiwei Xie, Keqiang Huang, Qiujiang Guo, Libo Zhang, Pengfei Zhang, Da Xu, Dongning Zheng, Xiaobo Zhu, H. Wang, Y.-A. Chen, C.-Y. Lu, Siyuan Han, J.-W. Pan, "10-qubit entanglement and parallel logic operations with a superconducting circuit". arXiv:1703.10302 (2017). 

Achieving 200 km of Measurement-device-independent Quantum Key Distribution with High Secure Key Rate

[Left to Right] Hualei Yin, Tengyun Chen, Yanlin Tang.

Authors: Yan-Lin Tang^1,2, Hua-Lei Yin^1,2, Si-Jing Chen³, Yang Liu^1,2, Wei-Jun Zhang³, Xiao Jiang^1,2, Lu Zhang³, Jian Wang^1,2, Li-Xing You³, Jian-Yu Guan^1,2, Dong-Xu Yang^1,2, Zhen Wang³, Hao Liang^1,2, Zhen Zhang^2,4, Nan Zhou^1,2, Xiongfeng Ma^2,4, Teng-Yun Chen^1,2, Qiang Zhang^1,2, Jian-Wei Pan^1,2

Affiliation:
¹National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, Shanghai Branch, University of Science and Technology of China, Hefei, China,
²CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, Shanghai Branch, University of Science and Technology of China, Hefei, China,
³State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, China,
⁴Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China.

 Information security is a long-standing problem in history. Nowadays, with the developing requirement of information transmission, the security becomes a much more sensitive problem. By leveraging the laws of quantum Mechanics, Quantum Key Distribution (QKD) [1] can provide a solution for information-theoretical security. As the most practical application of quantum information technology, it is under rapid development in both theoretical and experimental aspects. Besides the standard BB84 protocol, various protocols are proposed subsequently to adapt to different situations. Meanwhile, the QKD systems are successfully transformed from controlled laboratory environments to real-life implementations, and quite a few commercial QKD systems are available in the market up till now.

Past 2Physics article by Jian-Wei Pan :
June 30, 2013: "Quantum Computer Runs The Most Practically Useful Quantum Algorithm" by Chao-Yang Lu and Jian-Wei Pan.

Despite these tremendous developments, real-world QKD systems still suffer from various attacks [2-4] which explore the loopholes rooted in the deviations of practical implementations from the theoretical models in security proofs. Most of these attacks are targeting at the measurement devices. Among them, the first successful attack is the time-shift attack [3] which explores the loophole of time-dependent efficiency mismatch of two detectors. The most powerful kind of attacks is the detector-blinding attack [4], which fools the detector to work in the unwanted linear mode and forces them to act according to Eve’s will. Although certain countermeasures are provided to close some specific side channels, there might still be some side channels which are hard to estimate and will cause potential threats. So we are looking for an effective solution to close these loopholes once and for all.

Fortunately, Measurement-Device-Independent Quantum Key Distribution (MDIQKD) was invented by H-.K-. Lo in 2012 [5] to remove all side channels from the most vulnerable measurement unit. This protocol is inspired by the time-reversed EPR protocol [6], and it does not rely on any measurement assumption and can thus close all the measurement loopholes once and for all. Since its invention, it has attracted worldwide attention, and has been successfully demonstrated based on various MDIQKD systems, including polarization encoding system [7,8] and time-bin phase-encoding system [9,10]. In view of the performance, these previous MDIQKD demonstrations have limitations as well, such as short distance and a poor key rate (the best is 0.1 bps@50km [10]). This is so because the critical element of MDIQKD protocol is the Bell-state measurement, which requires both perfect interference of two independent laser sources and efficient two-fold coincidence detection. It imposes severe technical challenges on the laser modulation, high-efficiency detection and system stabilization. Therefore, based on the previous results and the intrinsic requirements of MDIQKD, people might still wonder that this ingenious protocol is a fancy but impractical idea.

In this recent work published in Physical Review Letters [11] by our group, we have extended the MDIQKD secure distance to state-of-the-art 200 km, comparable with the limit of regular decoy-state BB84 protocol. The secure key rate is almost three orders of magnitude higher than the previous results of MDIQKD demonstrations. These results are achieved with a fully-automatic highly-stable 75 MHz system and high-efficiency superconducting single photon detectors (SNSPDs), as shown in Fig. 1. We also employ an optimized decoy-state scheme and new post-processing method with a much lower failure probability than previous ones.

Fig.1: (a) Schematic layout of our MDIQKD setup. Alice's (Bob's) signal laser pulses (1550 nm) are modulated into three decoy-state intensities by AM1. An AMZI, AM2~4 and one PM are to encode qubits. Charlie's setup consists of a polarization stabilization system and a BSM system. The polarization stabilization system in each link includes an electric polarization controller (EPC), a polarization beam splitter (PBS) and an InGaAs/InP single-photon avalanche photodiode (SPAPD). The BSM system includes an interference BS and two SNSPDs. (b) Time calibration system. Two synchronization lasers (SynL, 1570 nm) are adopted, with the 500 kHz shared time reference generated from a crystal oscillator circuit (COC) and with the time delayed by a programmable delay chip (PDC). Alice (Bob) receives the SynL pulses with a photoelectric detector (PD) and then regenerates a system clock of 75 MHz. WDM: wavelength division multiplexer, ConSys: control system. (c) Phase stabilization system. Circ: circulator, PC: polarization controller, PS: phase shifter.

This is the first time we increase the repetition rate to 75 MHz, compared with 1MHz of our previous demonstration [10]. The repetition rate improvement owes to the laser source with good waveform, the high-speed electrical control system, and the superconducting single photon detector with a small time jitter of a few 10 ps [12]. In terms of high-speed laser modulation, we remark that the speed improvement for MDIQKD is not as easy as that for regular BB84 protocol, since the indistinguishability of two independent laser sources has some subtle requirements for laser modulation. Firstly, we should adopt direct laser modulation to ensure the phase is intrinsically randomized to avoid the unambiguous-state-discrimination attack [13]. The problem is that in a high-speed situation, the current mutation will induce severe overshoot, ringing and chirp inside the laser pulse. Especially, the chirp adds an extra phase at the tail of our laser pulse. Thus, we cut off the tail part by an amplitude modulator (AM), to optimize the laser interference and ensure the waveform indistinguishability. Secondly, regarding the vacuum state modulation (based on the vacuum+weak decoy state scheme), we should take the influence of the direct laser modulation into consideration, which is not a severe problem for regular BB84 protocol. We find that when we randomly modulate some laser pulses into vacuum state by not sending triggering signal to the laser (namely direct laser modulation), the interference visibility will decrease to a very bad level. This is because of the aperiodic triggering signals to the laser which introduce large temperature fluctuation and wavelength fluctuation. The wavelength fluctuation thus causes imperfect interference. To avoid this effect, instead of direct vacuum modulation, we adopt an alternative method of external vacuum modulation by AM. We utilize three AMs, within which only one is for decoy state encoding, and the other two are mainly used for qubit encoding and are also beneficial to decrease the vacuum intensity. Thus a high extinction ratio of the vacuum state of more than 10000 : 1 is achieved.

This is also the first time superconducting nanowire single-photon detectors (SNSPD), one of the best single photon detectors at near-infrared (NIR) wavelengths, is applied in an MDIQKD system. Since the BSM, the essence of MDIQKD, requires two-fold coincidence detection, the key rate is proportional to the square of detection efficiency. In our experiment, operated below 2.2 K with a Gifford-McMahon cryocooler, two SNSPDs with detection efficiencies of 40% and 46% largely improve the key rate. Besides, the low dark count rate of 10 Hz helps to achieve an enough signal-to-noise ratio even at 200 km distance. Besides the high detection efficiency and low dark count, there is another important property, small timing jitter of a few 10 ps, which is beneficial for QKD performance, especially the system timing jitter and repetition rate. We can expect an improvement of 1 GHz up to 10 GHz MDIQKD system adopting the SNSPD in the near future.

Another important element for achieving 200 km distance is the system stabilization. Since the 200 km situation will make the system stability difficult because of the severe fiber fluctuation, and make it even harder with weak feedback signals due to large fiber attenuation. Besides, since the detection rate is slower in 200 km, we need more time to accumulate enough data required by strict fluctuation analysis. In short, we need our system to work in a worse environment for a longer time. Faced with these problems, we build a fully-automatic feedback system without manual efforts to precisely calibrate and stabilize all the parameters, such as the time, spectrum, polarization and the phase reference. Although the whole feedback system is a challenge in engineering, it is critical to enable continuous running and will be a necessary component in practical MDIQKD system.

Fig.2: Bird's-eye view of the field-environment MDIQKD. Alice is placed in Animation Industry Park in Hefei (AIP), Bob in an office building (OB), and Charlie in the University of Science and Technology of China (USTC). Alice (Bob) is on the west (east) side of Charlie. AIP-USTC link is 25 km (7.9 dB), and OB-USTC link is 5 km (1.3 dB).

To further show the practical value of MDIQKD in an unstable environment, we have moved the system into installed fiber network and implemented a field test as shown in Fig. 2 [14]. Previously, an MDIQKD field test was attempted over an 18.6 km deployed fiber, however, a secure key was not actually generated since random modulated decoy state was not performed. In comparison, our field test strictly adopts the decoy-state scheme to guarantee the source security. With optimized decoy-state parameters and Chernoff bound in strict fluctuation analysis with tight failure probability of 2×10⁻⁹, we have achieved secure key rates of 67 bps (@50km in the laboratory for 130.0 hours) and 17 bps (@30km in the field test for 18.2 hours), shown in Fig.3, which are at least two orders of magnitude higher than previous results.

Fig. 3: Secure key rates of experiments in the laboratory and in the field test, as well as the simulation results. The four dots correspond to the experimental results with the fiber transmitting loss of 9.9 dB (50 km), 19.9 dB (100 km), 29.8 dB (150 km) and 39.6 dB (200 km). The solid curve shows the result calculated by simulating the vacuum+weak decoy state scheme with the experimental parameters. The dashed curve represents the optimal result with infinite number of decoy states. The square marks the field test result, which is 17 bps. Also shown are results from the previous demonstration for comparison.

These technological advances in our work constitute a critical ingredient for quantum repeater [15], the core resource for long distance quantum communication. Besides, the MDIQKD protocol has an intrinsic property which is desirable for constructing quantum network [16] with the star-type structure. We can place the expensive detection system in the server node to perform the BSM operation, and all the users can share this system. Furthermore, the techniques of stable BSM we developed have many other applications, such as quantum teleportation [17] and quantum fingerprinting [18].

References:
[1] Charles H. Bennett and Gilles Brassard, "Quantum cryptography: Public key distribution and coin tossing”, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (Bangalore, India, 1984), pp. 175–179. Full Article.
[2] Chi-Hang Fred Fung, Bing Qi, Kiyoshi Tamaki, Hoi-Kwong Lo, “Phase-remapping attack in practical quantum-key-distribution systems”. Physical Review A, 75, 032314 (2007). Abstract.
[3] B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems”, Quantum Information & Computation, 7, 073 (2007).
[4] Lars Lydersen, Carlos Wiechers, Christoffer Wittmann, Dominique Elser, Johannes Skaar, Vadim Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination”, Nature Photonics, 4, 686 (2010). Abstract.
[5] Hoi-Kwong Lo, Marcos Curty, Bing Qi, “Measurement-Device-Independent Quantum Key Distribution”, Physical Review Letters, 108, 130503 (2012). Abstract.
[6] Eli Biham, Bruno Huttner, Tal Mor, “Quantum cryptographic network based on quantum memories”. Physical Review A, 54, 2651 (1996). Abstract.
[7] Zhiyuan Tang, Zhongfa Liao, Feihu Xu, Bing Qi, Li Qian, Hoi-Kwong Lo, “Experimental Demonstration of Polarization Encoding Measurement-Device-Independent Quantum Key Distribution”, Physical Review Letters, 112, 190503 (2014). Abstract.
[8] T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, J. P. von der Weid, “Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits”, Physical Review A, 88, 052303 (2013). Abstract.
[9] A. Rubenok, J. A. Slater, P. Chan, I. Lucio-Martinez, W. Tittel, “Real-World Two-Photon Interference and Proof-of-Principle Quantum Key Distribution Immune to Detector Attacks”, Physical Review Letters, 111, 130501 (2013). Abstract.
[10] Yang Liu, Teng-Yun Chen, Liu-Jun Wang, Hao Liang, Guo-Liang Shentu, Jian Wang, Ke Cui, Hua-Lei Yin, Nai-Le Liu, Li Li, Xiongfeng Ma, Jason S. Pelc, M. M. Fejer, Cheng-Zhi Peng, Qiang Zhang, Jian-Wei Pan, “Experimental Measurement-Device-Independent Quantum Key Distribution”. Physical Review Letters, 111, 130502 (2013). Abstract.
[11] Yan-Lin Tang, Hua-Lei Yin, Si-Jing Chen, Yang Liu, Wei-Jun Zhang, Xiao Jiang, Lu Zhang, Jian Wang, Li-Xing You, Jian-Yu Guan, Dong-Xu Yang, Zhen Wang, Hao Liang, Zhen Zhang, Nan Zhou, Xiongfeng Ma, Teng-Yun Chen, Qiang Zhang, Jian-Wei Pan, “Measurement-device-independent quantum key distribution over 200 km”. Physical Review Letters, 113, 190501 (2014). Abstract.
[12] Xiaoyan Yang, Hao Li, Weijun Zhang, Lixing You, Lu Zhang, Xiaoyu Liu, Zhen Wang, Wei Peng, Xiaoming Xie, Mianheng Jiang, “Superconducting nanowire single photon detector with on-chip bandpass filter”, Optics Express, 22, 16267 (2014). Abstract.
[13] Yan-Lin Tang, Hua-Lei Yin, Xiongfeng Ma, Chi-Hang Fred Fung, Yang Liu, Hai-Lin Yong, Teng-Yun Chen, Cheng-Zhi Peng, Zeng-Bing Chen, Jian-Wei Pan, “Source attack of decoy-state quantum key distribution using phase information”, Physical Review A, 88, 022308 (2013). Abstract.
[14] Yan-Lin Tang, Hua-Lei Yin, Si-Jing Chen, Yang Liu, Wei-Jun Zhang, Xiao Jiang, Lu Zhang, Jian Wang, Li-Xing You, Jian-Yu Guan, Dong-Xu Yang, Zhen Wang, Hao Liang, Zhen Zhang, Nan Zhou, Xiongfeng Ma, Teng-Yun Chen, Qiang Zhang, Jian-Wei Pan, “Field Test of Measurement-Device-Independent Quantum Key Distribution”, arXiv:1408.2330 [quant-ph] (2014).
[15] H.-J. Briegel, W. Dür, J. I. Cirac, P. Zoller, “Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication”, Physical Review Letters, 81, 5932 (1998). Abstract.
[16] Jane Qiu, “Quantum communications leap out of the lab”, Nature, 508, 441 (2014). Article.
[17] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, William K. Wootters, “Teleporting an unknown quantum state via dual classic and Einstein-Podolsky-Rosen channels”, Physical Review Letters, 70, 1895 (1993). Abstract.
[18] Harry Buhrman, Richard Cleve, John Watrous, Ronald de Wolf, “Quantum Fingerprinting”, Physical Review Letters, 87, 167902 (2001). Abstract.

Airborne Demonstration of a Quantum Key Distribution Receiver Payload

Christopher J. Pugh (left) and Thomas Jennewein

Authors: Christopher J. Pugh^1,2, Brendon L. Higgins^1,2,  Thomas Jennewein^1,2

Affiliation:
¹Institute for Quantum Computing, University of Waterloo, Ontario, Canada
²Dept of Physics and Astronomy, University of Waterloo, Ontario, Canada.

Quantum safe cryptography has truly been thrust into the limelight recently, especially after the NSA announced “The Information Assurance Directorate (IAD) will initiate a transition to quantum resistant algorithms in the not too distant future,” in August of 2015. Previous to this announcement, there has been a multitude of work done in accomplishing the quantum key distribution (QKD) protocol [1], a symmetric key algorithm, which has been proven to be cryptanalytically secure, even against quantum computer attacks. One major concern with QKD is the distances over which secure keys can be generated. In optical fibers this is known to have an upper limit around a few hundred kilometers due to absorption in the fibers. For free space, we are limited in line of site as well as atmospheric turbulence.

Using satellites to assist in the key generation helps alleviate these distance concerns by linking multiple stations located on the ground which can be separated by much larger distances than allowed by ground links. Performing QKD with moving platforms are important to prove the viability of future satellite implementations. Demonstrations of QKD to aircraft, prior to this work, have operated in the downlink configuration [2,3], where the quantum source and transmitter are placed on the airborne platform. Most recently, the Chinese Micius satellite performed entanglement distribution to ground stations separated by at least 1200 kilometers which has shown the viability of using satellites for quantum information purposes [4]. While the downlink approach ultimately has the potential for higher key rate, it is more complex and is not as flexible as an uplink configuration, which places the quantum receiver on the airborne platform while keeping the quantum source at the ground station [5]. In September 2016, we successfully achieved a quantum uplink, generating quantum secure key, to an airplane [6].

Our experimental setup consists of a QKD source (in a trailer for temperature and humidity control) and transmitter located at a ground station at Smiths Falls—Montague Airport (Fig 1), and a QKD receiver located on a Twin Otter research aircraft from the National Research Council of Canada. Targeting and tracking were established using strong beacon lasers, an imaging camera, and tracking feedback to motors at each of the two sites. Once at the aircraft, the QKD signals were recorded for later processing to complete the QKD protocol and secure extract key.

In order to generate the photons for encoding the information, we use a weak coherent pulse source implementing polarization-encoded BB84 with decoy states [7] at a rate of 400 MHz. These signals are characterized at the source with an automated polarization compensation system to compensate for drifts due to the optical fiber portion of the transmission to the transmitting telescope.

Fig 1: Optical ground station located at Smiths Falls—Montague Airport. The airplane is shown in the background as the white dashed line in the sky.

At the receiver, the signal is coupled from the receiver telescope into a custom fine pointing unit which guides both the quantum and beacon signals with a fast-steering mirror. Inside the fine-pointing system, a dichroic mirror separates the quantum and beacon signals---the beacon is reflected towards a quad-cell photo-sensor, providing position feedback to guide the fast-steering mirror in a closed loop.

The quantum signal then passes into a custom integrated optical assembly, containing a passive-basis-choice polarization analysis module with a 50:50 beam splitter and polarizing beam splitters, resulting in four beams corresponding to the four BB84 measurement states (horizontal, vertical, diagonal, and anti-diagonal). These four modes are then coupled into multimode fibers and guided to Silicon avalanche photo diodes detectors. The detectors trigger low-voltage differential signalling pulses which are measured at a control and data processing unit based on Xiphos' Q7 processor card, which has recently flown on the GHGSat, with a custom daughter board.

The airplane flew two path types: circular arcs around the ground station, and lines past the ground station. The distances for each type of pass varied from 3 to 10 km. The circular paths were used for longer link times as well as to relax pointing requirements as the aircraft telescope would remain relatively still and the transmitter would observe a constant rate. The line passes are more representative of a satellite, showing different angular speeds for different portions of the pass.

Fig 2: The Smiths Falls—Montague Airport as seen from the airplane during a day test flight. The end of the telescope can be seen in the far left of the photo.

In total, we had successful quantum links in seven of 14 passes of the airplane over the ground station, generating asymptotic key in one pass and finite-size secure key in 5 passes, with one pass showing over 800 kbit. The loss in the various passes ranged from 34.4 to 51.1 dB. Angular speeds (at the transmitter) between 0.4 deg/s and 1.28 deg/s were achieved. A transmitter pointing at a typical low-Earth-orbit satellite with an altitude of roughly 600 kilometers would be tracking at an angular speed of approximately 0.7 deg/s whereas tracking the International Space Station would require approximately 1.2 deg/s.

Fig 3: (left to right) Christopher Pugh and Thomas Jennewein hold up a University of Waterloo/Institute for Quantum Computing sticker to be mounted on the NRC Twin Otter Research Aircraft. The QKD receiver can be seen in the open door of the airplane.

In this experiment, we have demonstrated the viability of components of a quantum receiver satellite payload by successfully performing quantum key distribution in an uplink configuration to an airplane. The major components in the receiver payload (fine pointing unit, integrated optics assembly, detector modules, control and data processing unit) have a clear path to flight for future satellite integration. Recently, the Canadian government and the Canadian Space Agency have announced the intent to build a quantum satellite and this work will be beginning shortly.

References:
[1] Charles H. Bennett and Gilles Brassard, “Quantum cryptography: Public key distribution and coin tossing”. In Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, pages 175-179 (IEEE Press, New York, 1984). Article.
[2] Sebastian Nauerth, Florian Moll, Markus Rau, Christian Fuchs, Joachim Horwath, Stefan Frick, Harald Weinfurter, “Air-to-ground quantum communication”. Nature Photonics, 7, 382 (2013). Abstract.
[3] Jian-Yu Wang, Bin Yang, Sheng-Kai Liao, Liang Zhang, Qi Shen, Xiao-Fang Hu, Jin-Cai Wu, Shi-Ji Yang, Hao Jiang, Yan-Lin Tang, Bo Zhong, Hao Liang, Wei-Yue Liu, Yi-Hua Hu, Yong-Mei Huang, Bo Qi, Ji-Gang Ren, Ge-Sheng Pan, Juan Yin, Jian-Jun Jia, Yu-Ao Chen, Kai Chen, Cheng-Zhi Peng, Jian-Wei Pan., “Direct and full-scale experimental verifications towards ground-satellite quantum key distribution”. Nature Photonics, 7, 387 (2013). Abstract.
[4] Juan Yin, Yuan Cao, Yu-Huai Li, Sheng-Kai Liao, Liang Zhang, Ji-Gang Ren, Wen-Qi Cai, Wei-Yue Liu, Bo Li, Hui Dai, Guang-Bing Li, Qi-Ming Lu, Yun-Hong Gong, Yu Xu, Shuang-Lin Li, Feng-Zhi Li, Ya-Yun Yin, Zi-Qing Jiang, Ming Li, Jian-Jun Jia, Ge Ren, Dong He, Yi-Lin Zhou, Xiao-Xiang Zhang, Na Wang, Xiang Chang, Zhen-Cai Zhu, Nai-Le Liu, Yu-Ao Chen, Chao-Yang Lu, Rong Shu, Cheng-Zhi Peng, Jian-Yu Wang, Jian-Wei Pan, “Satellite-based entanglement distribution over 1200 kilometers”. Science, 356:1140 (2017). Abstract.
[5] J-P Bourgoin, E Meyer-Scott, B L Higgins, B Helou, C Erven, H Hübel, B Kumar, D Hudson, I D'Souza, R Girard, R Laflamme, T. Jennewein, “A comprehensive design and performance analysis of low Earth orbit satellite quantum communication”. New Journal of Physics, 15, 023006 (2013). Abstract.
[6] Christopher J Pugh, Sarah Kaiser, Jean-Philippe Bourgoin, Jeongwan Jin, Nigar Sultana, Sascha Agne, Elena Anisimova, Vadim Makarov, Eric Choi, Brendon L Higgins, Thomas Jennewein, “Airborne demonstration of a quantum key distribution receiver payload”. Quantum Science and Technology, 2, 024009 (2017). Abstract.
[7] Hoi-Kwong Lo, Xiongfeng Ma, Kai Chen, “Decoy state quantum key distribution”. Physical Review Letters, 94, 230504 (2005). Abstract.