One-shot lossy quantum data compression

Abstract

We provide a framework for one-shot quantum rate distortion coding, in which the goal is to determine the minimum number of qubits required to compress quantum information as a function of the probability that the distortion incurred upon decompression exceeds some specified level. We obtain a one-shot characterization of the minimum qubit compression size for an entanglement-assisted quantum rate-distortion code in terms of the smooth max-information, a quantity previously employed in the one-shot quantum reverse Shannon theorem. Next, we show how this characterization converges to the known expression for the entanglement-assisted quantum rate distortion function for asymptotically many copies of a memoryless quantum information source. Finally, we give a tight, finite blocklength characterization for the entanglement-assisted minimum qubit compression size of a memoryless isotropic qubit source subject to an average symbol-wise distortion constraint.

36 pages

References in corpus (6)

• Coding Theorem and Strong Converse for Quantum Channels
• The mother of all protocols: Restructuring quantum information's family tree
• Smooth Max-Information as One-Shot Generalization for Mutual Information
• Generalized Entropies
• Quantum rate distortion coding with auxiliary resources
• Quantum-to-classical rate distortion coding

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• Entanglement-assisted private communication over quantum broadcast channels
• Quantum Rate-Distortion Coding of Relevant Information
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