Quantum Teleportation of Multiple Properties of A Single Quantum Particle
Authors: Chao-Yang Lu, Jian-Wei Pan
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  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.  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.
Although extensive efforts have been undertaken in the experimental demonstrations of teleportation in various physical systems, including photons , atoms , ions , electrons , and superconducting circuits , 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 4N (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 . 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
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.
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