Source coding with quantum side information at several decoders

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.

Masahito Hayashi

John Watrous

Shraga I. Bross

In the secure cooperative source-coding problem that we consider, Encoder 1 and Decoder 1 observe, respectively, a pair of independent identically distributed (i.i.d.) correlated sources and wish to communicate the first source to Decoder 2 subject to a distortion constraint. Encoder 1 sends a message to both the decoders over a public nonsecure channel, and then Decoder 1-the helper-sends a message just to Decoder 2 over a secure channel. An eavesdropper, which has access to memoryless side-information that is correlated with the first source, intercepts the message sent by Encoder 1 and based on both wishes to minimize its uncertainty about the first source. The secrecy measure of the system is the equivocation of the first source at the eavesdropper. We determine the rates equivocation region for this problem assuming that conditioned on the side-information of Decoder 1 the eavesdropper's side-information is independent of the first source. To that end, we derive an inner and an outer bound that depend explicitly on the proportional rate that Encoder 1 spends in the cooperation process. Subsequently, we evaluate this region for the case of a doubly symmetric binary source and Hamming distortion.

François Chapeau‐Blondeau

Min-Hsiu Hsieh, Shun Watanabe

We study classical source coding with quantum side-information where the quantum side-information is observed by a helper and sent to the decoder via a classical channel. We derive a single-letter characterization of the achievable rate region for this problem. The direct part of our result is proved via the measurement compression theory by Winter. Our result reveals that a helper's scheme that separately conducts a measurement and a compression is suboptimal, and the measurement compression is fundamentally needed to achieve the optimal rate region.