Source Coding in Quantum Systems

John Watrous

Xu Han, Xiaomin Liu, Zhengjun Xi

Tomohiko Uyematsu, Tetsunao Matsuta

A source coding system with side information at the decoder is a typical multiterminal source coding system where output sequences of two sources are independently encoded, but a decoder recovers only one output sequence from two codewords. Since Wyner, Ahlswede and Körner independently investigated this system, we call it as the WAK coding system. This paper investigates the ε-achievable rate region of the WAK coding system which allows the probability of error within a fixed tolerance ε(∈ (0, 1)), and clarifies the ε-achievable rate region for correlated general sources in terms of the smooth max-entropy and the smooth max Rényi divergence. To this end, we show a new one-shot converse theorem for the WAK coding system, and a one-shot covering lemma which is a refined version of Warsi's result. Then, combining these results, we clarify the ε-achievable rate region of the WAK coding system.

François Chapeau‐Blondeau

Xiaomin Liu, Feiran Cheng, Zhengjun Xi

In this paper, we introduce an information-theoretic task that we refer to as correlated sources coding where decoders possess complementary quantum side information. We present the optimal rates for lossless correlated sources coding with both complementary and less noisy quantum side information. We also generalize quantum Sgarro's coding and correlated sources coding with complementary quantum side information to scenarios with distortion.

Hui Chen, Lizhen Wang

Considering the shortcomings of distributed source coding (DSC) in quantum communication, such as the high bit error rate and low compression ratio, an improved distributed source coding is proposed in this paper. In the design of the source encoder, redundancy technology is used to provide error protection, and then the joint design of Low-Density Parity Check code (LDPC) with redundancy is adopted to conduct distributed source coding. Experiment results show that the proposed method can be kept the compression ratio well and be easily implemented when a strong internal correlation of the quantum communication areas. The the reconstructed sequence can reach low bit error rate when the correlation between sources are weak. It is a practical, efficient DSC scheme.