The noiseless linear amplification for polarization-time-bin hyper-encoded coherent states
Yucai Zhu, Wenyi Zhu, Wei Zhong +3 more
Quantum communication is based on the basic principles of quantum mechanics such as the Heisenberg uncertainty and the no-cloning theorem. Quantum communication can detect the eavesdropping, so that it has unconditional security in theory. Coherent state is an important continuous-variable resource in the quantum communication field. The hyper-encoded coherent states mean encoding in two or more degrees of freedom (DOFs) of each photon in the coherent state, which can increase the capacity of single photon and has potential applications in future high-capacity quantum communication field. However, during practical applications, the channel noise may cause photon transmission loss, which will largely reduce quantum communication’s efficiency, even threaten its security. As a result, the photon transmission loss largely limits the applications of the hyper-encoded coherent states. The noiseless linear amplification (NLA) is a promising method to solve the photon transmission loss problem. However, no existing NLA schemes can be used for the hyper-encoded coherent states. In the paper, we propose an NLA protocol for arbitrary polarization-time-bin hyper-encoded coherent states assisted by auxiliary single photons. This NLA protocol adopts the quantum scissor (QS) devices in the parallel structure. The protocol first splits the input coherent state into N paths with the help of the first beam splitter array, which makes the coherent state in each path be a weak coherent state. Then, it applies the QS in each path. Only when the QS in each path obtains the successful photon-detector response, the whole NLA protocol will be successful. In this case, the output states in all paths will be finally converged into one output path with the help of the second beam splitter array. By adjusting the transmittance of the variable beam splitters in each QS, the NLA protocol can increase the average photon number of the output coherent state, and thus realize the amplification of the coherent state. Meanwhile, the hyper-encoded features in the polarization and time-bin DOFs can be perfectly preserved. Our NLA protocol only requires the common optical elements, so that it can be realized under current experimental conditions. Then, we analyze the performance of our NLA protocol with practical experimental conditions. First, the NLA protocol requires the photon-number-resolving detectors in theory, which are unavailable under practical experimental conditions. With practical imperfect photon detectors, which cannot distinguish the input photon number and have relatively low detection efficiency, the total success probability of the NLA protocol will decrease. Meanwhile, some unwanted disturb items may be introduced into the output state with a small probability, so that the fidelity of the target coherent state in the output state will decrease. Second, the NLA protocol requires an infinite N in theory. In practical experiments, we can only choose a finite N. In this way, besides the amplification, the NLA protocol will perform the N-photon truncation of the coherent state. With the growth of N, the fidelity of the output state will increase, but the total success probability of this NLA protocol will decrease. In conclusion, our NLA protocol can realize the amplification of the polarization-time-bin hyper-encoded coherent state and preserve the hyper-encoded features of the photons. Meanwhile, it can be realized under current experimental conditions. Our protocol has application potential in the future quantum communication field.
Chinese Science Bulletin (Chinese Version)•May 24, 2023•3 citations