Quantum-to-classical rate distortion coding

Abstract

We establish a theory of quantum-to-classical rate distortion coding. In this setting, a sender Alice has many copies of a quantum information source. Her goal is to transmit classical information about the source, obtained by performing a measurement on it, to a receiver Bob, up to some specified level of distortion. We derive a single-letter formula for the minimum rate of classical communication needed for this task. We also evaluate this rate in the case in which Bob has some quantum side information about the source. Our results imply that, in general, Alice's best strategy is a non-classical one, in which she performs a collective measurement on successive outputs of the source.

21 pages, 3 png figures, accepted for publication in Journal of Mathematical Physics

References in corpus (9)

• Quantum data processing and error correction
• Classical capacity of the lossy bosonic channel: the exact solution
• Continuity of quantum conditional information
• Classical data compression with quantum side information
• The information-theoretic costs of simulating quantum measurements
• "Extrinsic" and "intrinsic" data in quantum measurements: asymptotic convex decomposition of positive operator valued measures
• Quantum rate distortion, reverse Shannon theorems, and source-channel separation
• Compression of sources of probability distributions and density operators
• Quantum Rate-Distortion Theory for I.I.D. Sources

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• Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels
• Quantum Predictive Filtering
• The Wasserstein distance of order 1 for quantum spin systems on infinite lattices
• Efficient Computation of the Quantum Rate-Distortion Function
• Source Compression with a Quantum Helper
• Rate Reduction of Blind Quantum Data Compression with Local Approximations Based on Unstable Structure of Quantum States
• Fully Quantum Source Compression with a Quantum Helper
• A Rate-Distortion Perspective on Quantum State Redistribution
• Minimizing Quantum Renyi Divergences via Mirror Descent with Polyak Step Size
• Information-Theoretic Limits of Quantum Learning via Data Compression