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arXiv · 2502.12129

When Wyner and Ziv Met Bayes in Quantum-Classical Realm

Mohammad Aamir Sohail·Touheed Anwar Atif·S. Sandeep Pradhan
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Abstract

In this work, we address the lossy quantum-classical source coding with the quantum side-information (QC-QSI) problem. The task is to compress the classical information about a quantum source, obtained after performing a measurement while incurring a bounded reconstruction error. Here, the decoder is allowed to use the side information to recover the classical data obtained from measurements on the source states. We introduce a new formulation based on a backward (posterior) channel, replacing the single-letter distortion observable with a single-letter posterior channel to capture reconstruction error. Unlike the rate-distortion framework, this formulation imposes a block error constraint. An analogous formulation is developed for lossy classical source coding with classical side information (C-CSI) problem. We derive an inner bound on the asymptotic performance limit in terms of single-letter quantum and classical mutual information quantities of the given posterior channel for QC-QSI and C-CSI cases, respectively. Furthermore, we establish a connection between rate-distortion and rate-channel theory, showing that a rate-channel compression protocol attains the optimal rate-distortion function for a specific distortion measure and level.

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Mohammad Aamir Sohail, Touheed Anwar Atif, S. Sandeep Pradhan. 2025-02-17. When Wyner and Ziv Met Bayes in Quantum-Classical Realm. https://arxiv.org/abs/2502.12129

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