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2Physics

2Physics Quote:
"There is considerable evidence for the emergence of spatial dimensions in various settings, but there is no compelling evidence for the emergence of time. ... If time is emergent, some extension of the rules of quantum mechanics would seem to be required. The consistency of string theory requires that quantum mechanics is exactly correct. I am not questioning that this will continue to be the case in the future, only that quantum mechanics may need to be generalized somewhat to extend its domain of applicability."
-- John H. Schwarz (Read his article: "Superstring Theory: 5 Needed Breakthroughs" )

Sunday, February 22, 2015

Nonlocality and Conflicting Interest Games

[From Left to Right] Anna Pappa, Niraj Kumar, Thomas Lawson, Miklos Santha, Shengyu Zhang, Eleni Diamanti, Iordanis Kerenidis

Authors: Anna Pappa1,2, Niraj Kumar1,3, Thomas Lawson1, Miklos Santha2,4, Shengyu Zhang5, Eleni Diamanti1, Iordanis Kerenidis2,4

Affiliation:
1LTCI, CNRS–Télécom ParisTech, Paris, France, 
2LIAFA, CNRS–Université Paris 7, France, 
3Indian Institute of Technology, Kanpur, India, 
4CQT, National University of Singapore, Singapore, 
5Department of Computer Science and Engineering and ITCSC, The Chinese University of Hong Kong, Shatin, Hong Kong.

Nonlocality is a fundamental property of quantum mechanics that has puzzled researchers since the early formulations of quantum theory. Consider two parties, Alice and Bob, with inputs xA and xB respectively, who are positioned far from each other, and are asked to produce one output each (yA for Alice and yB for Bob). Even if the two players have pre-agreed on some local hidden variables, there exist quantum correlations that cannot be reproduced by any such set of variables [1,2]. These correlations allow the two parties to perform several computational tasks more efficiently, e.g. they can win specific games with probabilities strictly higher than allowed by any classical theory.

Till now, all known examples of quantum games considered players that have common interests, meaning that they either jointly win or lose the game. A famous such example is the CHSH game [3; CHSH stands for first letters of last names of the authors of this paper], where the players win if their outputs are different when both input bits are equal to 1, and if they are the same otherwise. It can be shown that classical resources provide a winning probability of 0.75, while the sharing of a maximally entangled pair can boost the winning probability to approximately 0.85. Another important type of games is conflicting interest games. A typical example is the “Battle of the Sexes”, where Alice and Bob want to meet, but Alice wants to go to the ballet, while Bob prefers theater. In case both go to the ballet, Alice is very pleased and Bob is fine with it; if they go to the theater, Bob is very pleased and Alice is fine with it, while if they go to different places, they are both very unhappy.

In our recent work [4], we examine whether the nonlocal feature of quantum mechanics can offer an advantage similar to the one observed in the CHSH game, but for games with conflicting interests. In order to observe a quantum advantage, we will study games with incomplete information (or Bayesian games), where each party receives some input unknown to the other party [5]. We present a Bayesian game with conflicting interests, and we show that there exist quantum strategies with average payoff for the two players strictly higher than that allowed by any classical strategy. The payoffs of the players for different inputs can be viewed as a table: the rows correspond to the outputs/actions of Alice (yA), while the columns to the outputs/actions of Bob (yB).
The players are interested in maximizing their average payoff over the probability distribution of their inputs, and they may use some advice from a third party (source) in order to achieve their goal. This advice can be in the form of classical bits or quantum states. In general, the classical bits received by the two players can be correlated between them (for example they can be either 00 or 11), and the quantum states may be entangled. By examining all possible strategies with classical advice, it is not difficult to verify that in our game, the sum of the average payoffs of the two players cannot be more than 1.125.

On the other hand, if we consider the case where quantum advice is given to the two players in the form of a maximally entangled state (Bell pair), the players can use projective measurements on their part of the state [6], in order to boost the sum of their average payoffs to 1.28, which is higher than any strategy with classical advice can achieve. It is very interesting to note here that the strategy that attains this payoff is also a quantum equilibrium, meaning that no player can gain a higher payoff by choosing a different strategy unilaterally.

Finally, we have demonstrated our game in practice, using the commercial entangled photon source quED by QuTools and taking a large number of independent runs of the game, in order to estimate each player’s average payoff. We found that the joint payoff is 1.246, which is well above the classical bound of 1.125, and slightly below the maximum value allowed by quantum strategies (1.28), because of experimental noise.

In conclusion, we demonstrated that the nonlocal feature of quantum mechanics can offer an advantage in a scenario where the two parties have conflicting interests. We examined a Bayesian game that attains higher payoffs for both players when using quantum advice compared to any classical strategy, and we experimentally verified the quantum advantage, by playing the game using a commercial photon source.

References:
[1] John Bell, "On the Einstein Podolsky Rosen paradox". Physics, 1, 195-200 (1964). Full Article.
[2] Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, Stephanie Wehner, “Bell nonlocality”, Review of Modern Physics, 86, 419 (2014). Abstract.
[3] John F. Clauser, Michael A. Horne, Abner Shimony, Richard A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories”. Physical Review Letters, 23, 880–884 (1969). Abstract.
[4] Anna Pappa, Niraj Kumar, Thomas Lawson, Miklos Santha, Shengyu Zhang, Eleni Diamanti, Iordanis Kerenidis, "Nonlocality and Conflicting Interest Games", Physical Review Letters, 114, 020401 (2015). Abstract.
[5] J. C. Harsanyi, Management Science, 14 (3), 159-183 (Part I), 14 (5): 320-334 (Part II), 14 (7): 486-502 (Part III) (1967/1968).
[6] Richard Cleve, Peter Høyer, Ben Toner, John Watrous, "Consequences and limits of nonlocal strategies", Proceedings of the 19th Annual IEEE Conference on Computational Complexity, pages 236–249 (2004). Full Article.

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Sunday, February 15, 2015

Homeostasis and dynamic phase transition in a simple model of cells with chemical signaling:
Can renormalization group teach us something nontrivial about biology?

Anatolij Gelimson (left) and Ramin Golestanian

Authors: Anatolij Gelimson, Ramin Golestanian

Affiliation: Rudolf Peierls Centre for Theoretical Physics, University of Oxford, United Kingdom.

The motility of bacteria or cells in response to chemicals (chemotaxis) has attracted a lot of interest in biological and medical research [2]. It plays a crucial role in cancer metastasis [3], the early stages of bacterial colony formation, wound healing and development of embryos [2]. However, the underlying mechanisms of these important processes are not fully understood due to the high complexity of these living many-body systems.

Figure 1: The interplay between the two general processes growth and chemotaxis (figure 1) leads to a variety of collective phenomena.

In our recent publication [1] in Physics Review Letters we have developed a simple model to shed some light on these interacting cells, also taking into account cellular growth and death. To study it, we have applied the method of so-called Dynamical Renormalization Groups common for the theory of phase transitions [4]. Similar to physical systems, it turns out that details of the microscopic behavior of cells do not impact the collective behavior on a large scale, whereas the interplay between the two general processes growth and chemotaxis (figure 1) leads to a variety of collective phenomena, which includes a sharp transition from a phase that has moderate controlled growth and death, and regulated chemical interactions, to a phase with strong uncontrolled growth/death and no chemical interactions [1]. Remarkably, for a range of parameters, the transition point shows nontrivial collective motion, which can even be described analytically. [1]

Bacteria such as E. coli have developed an elaborate run-and-tumble search strategy for the needed chemicals by coupling sensing of the chemicals to their motility machinery [5]. In eukaryotic cells, the chemotaxis mechanism is even more complex, often involving thousands of molecular motors or actin polymerization [6].

However, if one regards the effects of these microscopic mechanisms on a more macroscopic level, the resulting motion of bacteria and cells can effectively be modeled as a directed motion towards (or away from) increasing concentrations of chemicals [7]. On this coarse-grained level of description, the motion of bacteria in a field of chemicals is therefore somewhat analogous to the motion of particles in a gravitational or electrical field [8, 9].

But other than in non-active matter, distinctive features of a living system are also growth and death, which we need to take into account in a generic model for the formation of cellular or bacterial aggregations [10]. Interestingly, it turns out that the interplay between chemotactic interactions and growth-death processes leads to a range of different collective behaviors of cells.

We have studied our cellular model with the method of Dynamical Renormalization groups [4]. The basic idea behind it is simple: while microscopically a large number of particles, cells or bacteria might show very complicated behavior with a variety of different interactions, on a more macroscopic level only very few of these interactions will actually determine the collective effects. The so-called renormalization is basically a systematic way of observing a many-particle system from a coarser and coarser level. Coarsening the system will result in make some interactions disappear, whereas others will become stronger. In Physics, this development is called a flow in parameter space. [4]

Figure 2

In our model we have found a threshold in growth and chemotactic strength at which the flow in parameter space changes, which corresponds to a critical change of the macroscopic behavior of cells (figure 2). Below the threshold, the bacteria show jamming and aggregation due to chemotaxis. But above the threshold, chemotaxis becomes irrelevant and the behavior of cells is dominated by uncontrolled growth and death [1].

This threshold could potentially be tested experimentally and also contribute towards answering of fundamentally challenging questions in metastatic growth or bacterial colony formation. The hope is that our research will help understand what controls the communication between strongly dividing cells that are far apart and their collective behavior. The method of Dynamical Renormalization groups we have applied is very generic and could be powerful to shed light on more complex scenarios, like for example adhesive metastatic cells or chemical-dependent cell growth.

References:
[1] Anatolij Gelimson, Ramin Golestanian, "Collective Dynamics of Dividing Chemotactic Cells", Physical Review Letters, 114, 028101 (2015). Abstract.
[2] S.J. Singer, Abraham Kupfer, "The Directed Migration of Eukaryotic Cells", Annual Review of Cell Biology, 2, 337 (1986).
 Abstract.
[3] Douglas Hanahan, Robert A. Weinberg, Cell, 144, 646 (2011). Full Article.
[4] Ernesto Medina, Terence Hwa, Mehran Kardar, Yi-Cheng Zhang, "Burgers equation with correlated noise: Renormalization-group analysis and applications to directed polymers and interface growth", Physical Review A, 39, 3053 (1989). Abstract.

[5] Howard C. Berg, "E. coli in Motion" (Springer-Verlag, New York, 2004).
[6] Herbert Levine, Wouter-Jan Rappel, "The physics of eukaryotic chemotaxis", Physics Today, 66 (issue 2), 24 (2013). Abstract.

[7] Evelyn F. Keller, Lee A. Segel, "Traveling bands of chemotactic bacteria: A theoretical analysis", Journal of Theoretical Biology, 30, 235 (1971). 
Abstract.
[8] Pierre-Henri Chavanis, Carole Rosier, Clément Sire, "Thermodynamics of self-gravitating systems", Physical Review E, 66, 
036105 (2002). Abstract. 

[9] Pierre-Henri Chavanis, Clément Sire, "Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions", Physical Review E, 69, 016116 (2004). 
Abstract.
[10] Martin Nowak, "Evolutionary Dynamics", Harvard University Press (2006).

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Sunday, February 08, 2015

Building A Better Quantum Interface

From left to right: (top row) Bernardo Casabone, Konstantin Friebe, Birgit Brandstätter, (bottom row) Klemens Schüppert, Rainer Blatt, Tracy E. Northup.

Author: Konstantin Friebe

Affiliation: Institut für Experimentalphysik, Universität Innsbruck, Austria.

One of the largest challenges in quantum information science stems from the fact that to date no truly scalable quantum computer has been built, i.e., current devices only contain a few quantum bits (qubits). However, in order to access regimes where the power of quantum computation really comes into play, one would need scalable architectures with many qubits.

One approach for solving this issue is called distributed quantum computing. It consists of many small-scale quantum computers that are linked via photonic channels in close analogy to the internet or the “cloud” [1]. In this way, many small quantum computers can be linked together to make one large computer.

In this approach, the challenge consists of faithfully transferring quantum information between remote small-scale quantum computers via photonic channels. Quantum interfaces for this purpose can be built using cavity quantum electrodynamics systems. In such a system, the stationary qubits for computation are kept inside a cavity, also known as an optical resonator, i.e., between two mirrors. These mirrors enhance the interaction between the stationary qubits and photons (“flying qubits”), so that faithful transfer of quantum information from matter to light becomes possible. In fact, the mirrors make it possible to generate a single information-carrying photon from a stationary qubit and to be able to send this photon to another quantum computer with high efficiency [2].
Figure 1: Schematic of the setup. Two calcium ions (green spheres) are trapped inside an optical resonator (mirrors). By addressing the ions with laser beams at wavelengths 729 nm (global 729, addressing 729) and 393 nm, it is possible to prepare them in an entangled state with controllable phase, and a single photon can be generated in the cavity (red standing wave profile). The polarisation of the photon carries one qubit of information. After the photon has left the resonator, it is analysed using waveplates (λ/2, λ/4) and a polarising beam splitter (PBS), which splits up the two orthogonal polarisations H (horizontal) and V (vertical). The photon is then detected at one of two avalanche photodiodes (APD1 and APD2). (This Figure is from reference [3]).

In our recent experiment at the University of Innsbruck, Austria, we trapped two calcium ions inside an optical resonator [3]. In this case, the ions constitute the small-scale quantum computer. Ions are well-suited for this task, as an extensive toolbox for their preparation, manipulation and readout exists. The two ions were laser-cooled and prepared in an entangled state by manipulating their electronic and motional states with a laser field. Entanglement means that the two ions have “lost their individuality” and have to be described as a collective system with collective qualities. In this case, it is the electronic states of the two ions that are entangled with one another. This entangled state can be characterized by a phase, i.e., a number between zero and 2π. By controlling the phase of the entangled state of the two ions, it was possible to either enhance the probability to generate a photon in the cavity (phase 0) or to suppress the generation of a photon (phase π). The first case is called superradiance, while the suppression is called subradiance.
Figure 2: Probability of detecting a photon as a function of the time after the photon generation is started. The blue circles show the photon detection probability for the superradiant case (entangled state with phase 0), while the brown diamonds represent the subradiant state (entangled state with phase π). For comparison, the case of the two individual ions is shown (open triangles). For the superradiant case, the photon is produced faster than for a single ion, while in the subradiant case, photon generation is suppressed. Lines are simulations. (This Figure is from reference [3]).

We next encoded one qubit of information in the state of two entangled ions, that is, we used two “physical qubits” as a single “logical qubit”. The information stored in this qubit was then mapped onto the polarisation state of a single photon. By analysing the polarisation of the photon after it had left the resonator, we were able to show that the transfer of information was more faithful if the two ions were in the state with phase 0 than for a single ion. The efficiency of the process was higher, too.
Figure 3: Process fidelity (upper panel), the measure for the faithfulness of the transfer of quantum information, and efficiency (lower panel) as a function of the time after the photon generation is started. Blue filled circles are data from the superradiant entangled state, while open black circles are data from a single ion. Both process fidelity and efficiency are higher for the case of two entangled ions in the superradiant state. Lines are simulations. (This Figure is adapted from reference [3]).

In conclusion, by encoding quantum information in entangled states of more than one qubit, a better, i.e., more faithful quantum interface can be built, which is important for distributed quantum computing. Additionally, by choosing the phase π instead, qubits can be completely decoupled from the interface. This is interesting for future quantum computers consisting of long arrays of ions, where one might need a selective interface for just certain qubits, while the others remain undisturbed.

References:
[1] H. J. Kimble, "The quantum internet", Nature, 453, 1023 (2008). Abstract
[2] T.E. Northup, R. Blatt, "Quantum information transfer using photons", Nature Photonics, 8, 356 (2014). Abstract
[3] B. Casabone, K. Friebe, B. Brandstätter, K. Schüppert, R. Blatt, T. E. Northup, "Enhanced quantum interface with collective ion-cavity coupling", Physical Review Letters, 114, 023602 (2015). Abstract.
[4] C. Russo, H. G. Barros, A. Stute, F. Dubin, E. S. Phillips, T. Monz, T. E. Northup, C. Becher, T. Salzburger, H. Ritsch, P. O. Schmidt, R. Blatt, "Raman spectroscopy of a single ion coupled to a high-finesse cavity", Applied Physics B, 95, 205 (2009). Abstract.

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Sunday, January 25, 2015

Sound Velocity Bound and Neutron Stars

Paulo Bedaque (left) and Andrew W. Steiner (right)

Authors: Paulo Bedaque1, Andrew W. Steiner2,3,4 

Affiliation: 
1Department of Physics, University of Maryland, College Park, USA 
2Institute for Nuclear Theory, University of Washington, Seattle, USA
3Department of Physics and Astronomy, University of Tennessee, Knoxville, USA 
4Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA. 

Neutron stars are the final stage in the evolution of a star, the remnants of supernova explosion marking the end of the star’s life. They are incredibly compact objects: masses comparable to the Sun’s are compressed in a region of about 10 miles radius. At these densities, most matter is composed of neutrons. The repulsion between neutrons balances precariously against the strong gravitational fields generated by this high matter concentration: a little less repulsion or a little more mass leads to the collapse of the star into a black hole [1].

It has been possible to measure the mass of several neutron stars, and until recently, all accurate mass measurements were near 1.4 times the mass of our sun. However, within the past few years, two neutron stars have been discovered to have a mass around twice that of our sun [2]. What this discover means is that the neutron matter composing the star is stiffer than previously expected.

The speed of sound in air is about 346 meters per second, and it tends to increase with either the density or the temperature of the medium in which it travels. Since neutron stars contain the most dense matter in the universe one might wonder how fast the speed of sound is inside neutron stars.

Everywhere else in the universe [3], the speed of sound seems to be limited to the speed of light divided by the square root of 3, that is, v < 0.577 c (see, for example, the figures here: Link to plots >> ). At high enough densities or temperatures, the speed of sound approaches this limiting value. This result comes from quantum chromodynamics (QCD) [4] - the physical theory which describes how neutrons and protons (made of quarks) interact. At high enough densities and temperatures, QCD exhibits "asymptotic freedom", meaning that the interaction becomes weaker [5]. Unfortunately, neutron star densities are not large enough so that quarks are weakly interacting.

In a paper published in Physical Review Letters (as an 'Editor's suggestion') on January 21st [6], we showed that the speed of sound in neutron stars must exceed this value at some point inside a neutron star. The reason is that models where the speed of sound is smaller than the limiting value at all densities (those like the black lines in the figure) are too soft to produce neutron stars with masses twice the mass of the sun. Thus, the only alternative is that the speed of sound must look something like either the blue dotted or red dashed lines.

This result is important because it tells us more about how neutrons and protons interact, not only in neutron stars, but also here on earth [7]. It gives us more insight into how QCD behaves at high densities. Finally, it also helps us understand some of the more extreme neutron star-related processes like core-collapse supernovae, magnetar flares, and neutron star mergers.

Notes & References:
[1] See a diagram of stellar evolution from the Chandra X-ray observatory, their neutron star page, or the wikpedia entry on neutron stars.
[2] P.B. Demorest, T. Pennucci, S.M. Ransom, M.S.E. Roberts, J.W.T. Hessels, "A two-solar-mass neutron star measured using Shapiro delay". Nature, 467, 1081–1083 (2010). Abstract; John Antoniadis, Paulo C. C. Freire, Norbert Wex, Thomas M. Tauris, Ryan S. Lynch, Marten H. van Kerkwijk, Michael Kramer, Cees Bassa, Vik S. Dhillon, Thomas Driebe, Jason W. T. Hessels, Victoria M. Kaspi, Vladislav I. Kondratiev, Norbert Langer, Thomas R. Marsh, Maura A. McLaughlin, Timothy T. Pennucci, Scott M. Ransom, Ingrid H. Stairs, Joeri van Leeuwen, Joris P. W. Verbiest, David G. Whelan, "A Massive Pulsar in a Compact Relativistic Binary". Science, 340, 6131 (2013). Abstract.
[3] The only possible exception is matter inside the event horizon of a black hole, which is not causally connected with the rest of the universe anyway.
[4] See the Wikipedia article on Quantum Chromodynamics.
[5] This finding led to 2004 Nobel prize in physics for David J. Gross, H. David Politzer and Frank Wilczek.
[6] Paulo Bedaque, Andrew W. Steiner, "Sound Velocity Bound and Neutron Stars". Physical Review Letters, 114, 031103 (2015). Abstract. Also available at: arXiv:1408.5116 [nucl-th].
[7] Neutrons and protons are the basic building blocks of all atomic nuclei.

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Sunday, January 18, 2015

Novel Electromagnetic Cavities: Bound States in the Continuum

Thomas Lepetit (left) and Boubacar Kanté (right)

Authors: Thomas Lepetit and Boubacar Kanté 

Affiliation: Department of Electrical and Computer Engineering, University of California San Diego, USA. 

In the last 10 years, an intense research effort has been devoted to bringing all-optical signal generation and processing on chip to realize true photonic integrated circuits (PICs). PICs are at their core made of waveguides, which transfer signals to different devices on the circuit, and cavities, which process signals for different functionalities [1]. First, linear devices such as couplers, splitters, and add-drop filters were developed and, more recently, nonlinear devices such as frequency combs, nanolasers, and optical rams have been demonstrated [2-4]. Overall, progress has resulted in devices with increased functionalities that work at lower power and are more compact.

Cavities are an essential building block of PICs because they provide enhanced light-matter interaction. Currently, the most mature technology is based on a silicon on insulator platform and ring resonators. Typically, these dielectric resonators are several microns in diameter [5]. However, due to the difficulty of integration with much smaller electronic components, other technologies such as plasmonics have started to be investigated. One of the main advantages of plasmonic devices, which are made of noble metals such as gold and silver, is that their size is not limited by the wavelength. For example, plasmonic ring resonators of only several hundred nanometers in diameter have been demonstrated [6]. Generally, cavities are characterized by their quality factor Q, which is a measure of their capacity to store signals for a long time. At present, dielectric cavities have reached quality factors of 106, which are only limited by radiation losses coming from sidewall roughness, but typically have a footprint of 80 μm2. In contrast, plasmonic cavities can have a footprint as low as 1.25 μm2 but their quality factors are usually below 102, being limited by thermal losses coming from conduction electrons. Therefore, there is a need for novel cavity designs that can simultaneously achieve high quality factors and low footprints.
Figure 1: Cross-section of the electric field magnitude for the coupled resonators system (Half of it). Resonator 1, whose inner radius is zero, is on top and resonator 2, with a non-zero inner radius, is at the bottom. The symmetry plane on the right of each plot denotes the symmetry plane of interest. Odd modes are mostly confined in resonator 1 and even modes mostly in resonator 2.

Recently, we have demonstrated the possibility of making electromagnetic cavities using a different concept, namely bound states in the continuum (BICs) [7]. BICs were first proposed in 1929 in the context of quantum mechanics by Von Neumann and Wigner [8]. They surprisingly showed that bound states can exist above the continuum threshold, i.e., there are states that do not decay even in the presence of open decay channels. However, due to the theoretical nature of the first proposal, BICs did not become fully appreciated until 1985 when Friedrich and Wintgen showed that they could be interpreted as resulting from the interference of two distinct resonances [9]. In this picture, one resonance traps the other and thus one quality factor decreases while the other one tends to infinity. Since BICs are essentially a wave phenomenon they also appear in electromagnetics where they translate for lossless dielectrics into an infinite quality factor. As a proof of concept, we have designed and measured a BIC in the microwave range using a periodic metasurface [10-11].

BICs are intrinsically sensitive to perturbations as they only exist at a single point in phase space. This is very useful for sensing applications but detrimental for most others. To obtain an extended BIC, we designed a system with two quasi-degenerate BICs. We achieved this by considering a unit cell with two resonators, a disk and a ring (see Figure 1). Odd modes of the disk resonator interfere and lead to one BIC and even modes of the ring resonator interfere and lead to another BIC. We use ceramic resonators of high-permittivity (εr=43±0.75) and they are thus only slightly coupled. Experimentally, to limit the fabrication dispersion inherent to a large array, we made the measurements in a rectangular metallic waveguide (X-band, 8.2-12.4 GHz). It is possible because such a guided setup is equivalent to an infinite array at oblique incidence as shown by image theory.
Figure 2: Modes of two dielectric resonators (εr=43) in a rectangular metallic waveguide (X-band). Both resonators are cylindrical (r=3.5 mm, h1=2.25 mm, h2=3.0 mm) and the second has a non-zero inner radius. a) Resonance frequencies vs. inner radius for even and odd modes. b) Quality factor vs. inner radius for even and odd modes for lossless and lossy resonators.

We explored phase space along a line, by varying the inner radius of the ring resonator, and showed the presence of two avoided resonance crossings (see Figure 2a), which are typical of BICs [12]. As a result, there is an extended region of phase space where the quality factor tends to infinity (see Figure 2b). BICs only serve to cancel radiation losses and in the presence of thermal losses these are the limiting factor. At present, this scheme is therefore practical only for dielectrics but it could be extended to plasmonics by introducing gain materials to achieve loss-compensation.

Beyond the fundamental interest on the limit of quality-factors given a certain volume, there is a sustained interest in reducing the footprint of many cavity-based devices for future PICs. Tailoring the optical potential further, for example by moving away from perfectly periodic structures [13], opens the possibility improving the field confinement and thus shrink devices. Our work is a first step in this promising direction.

References:
[1] L. A. Coldren, S. W. Corzine, and M. Mašanović, “Diode Lasers and Photonic Integrated Circuits”, 2nd edition, Wiley (2012).
[2] Fahmida Ferdous, Houxun Miao, Daniel E. Leaird, Kartik Srinivasan, Jian Wang, Lei Chen, Leo Tom Varghese, Andrew M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs”, Nature Photonics, 5, 770 (2011). Abstract.
[3] M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, Y. Fainman, “Thresholdless nanoscale coaxial lasers”, Nature 482, 204 (2012). Abstract.
[4] Eiichi Kuramochi, Kengo Nozaki, Akihiko Shinya, Koji Takeda, Tomonari Sato, Shinji Matsuo, Hideaki Taniyama, Hisashi Sumikura, Masaya Notomi, “Large-scale integration of wavelength-addressable all-optical memories on a photonic crystal chip”, Nature Photonics 8, 474 (2014). Abstract.
[5] W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators”, Laser Photonics Review 6, 47 (2012). Abstract.
[6] Hong-Son Chu, Yuriy Akimov, Ping Bai, Er-Ping Li, “Submicrometer radius and highly confined plasmonic ring resonator filters nased on hybrid metal-oxide-semiconductor waveguide”, Optics Letters, 37, 4564 (2012). Abstract.
[7] Thomas Lepetit, Boubacar Kanté, “Controlling multipolar radiation with symmetries for electromagnetic bound states in the continuum”, Physical Review B Rapid Communications, 90, 241103 (2014). Abstract.
[8] J. von Neumann and E. Wigner, “On unusual discrete eigenvalues”, Zeitschrift für Physik 30, 465 (1929).
[9] H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum”, Physical Review A, 32, 3231 (1985). Abstract.
[10] Boubacar Kanté, Jean-Michel Lourtioz, André de Lustrac, “Infrared metafilms on a dielectric substrate”, Physical Review B, 80, 205120 (2009). Abstract.
[11] Boubacar Kanté, André de Lustrac, Jean Michel Lourtioz, “In-plane coupling and field enhancement in infrared metamaterial surfaces”, Physical Review B, 80, 035108 (2009). Abstract.
[12] Chia Wei Hsu, Bo Zhen, Jeongwon Lee, Song-Liang Chua, Steven G. Johnson, John D. Joannopoulos, Marin Soljačić, “Observation of trapped light within the radiation continuum”, Nature, 499, 188 (2013). Abstract.
[13] Yi Yang, Chao Peng, Yong Liang, Zhengbin Li, Susumu Noda, “Analytical perspective for Bound States in the Continuum in Photonic Crystal Slabs”, Physical Review Letters, 113, 037401 (2014). Abstract.

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Sunday, January 04, 2015

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 Tang1,2, Hua-Lei Yin1,2, Si-Jing Chen3, Yang Liu1,2, Wei-Jun Zhang3, Xiao Jiang1,2, Lu Zhang3, Jian Wang1,2, Li-Xing You3, Jian-Yu Guan1,2, Dong-Xu Yang1,2, Zhen Wang3, Hao Liang1,2, Zhen Zhang2,4, Nan Zhou1,2, Xiongfeng Ma2,4, Teng-Yun Chen1,2, Qiang Zhang1,2, Jian-Wei Pan1,2

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.

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