Quantum rate distortion coding with auxiliary resources

Abstract

We extend quantum rate distortion theory by considering auxiliary resources that might be available to a sender and receiver performing lossy quantum data compression. The first setting we consider is that of quantum rate distortion coding with the help of a classical side channel. Our result here is that the regularized entanglement of formation characterizes the quantum rate distortion function, extending earlier work of Devetak and Berger. We also combine this bound with the entanglement-assisted bound from our prior work to obtain the best known bounds on the quantum rate distortion function for an isotropic qubit source. The second setting we consider is that of quantum rate distortion coding with quantum side information (QSI) available to the receiver. In order to prove results in this setting, we first state and prove a quantum reverse Shannon theorem with QSI (for tensor-power states), which extends the known tensor-power quantum reverse Shannon theorem. The achievability part of this theorem relies on the quantum state redistribution protocol, while the converse relies on the fact that the protocol can cause only a negligible disturbance to the joint state of the reference and the receiver's QSI. This quantum reverse Shannon theorem with QSI naturally leads to quantum rate-distortion theorems with QSI, with or without entanglement assistance.

18 pages, 4 figures, IEEE format; v3: accepted into IEEE Transactions on Information Theory with minor changes

References in corpus (3)

• Remote preparation of quantum states
• The information-theoretic costs of simulating quantum measurements
• Quantum state redistribution based on a generalized decoupling

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• Quantum Rate-Distortion Coding of Relevant Information
• An upper bound on the second order asymptotic expansion for the quantum communication cost of state redistribution
• Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
• Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels
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• The Wasserstein distance of order 1 for quantum spin systems on infinite lattices
• Reliable Simulation of Quantum Channels: the Error Exponent
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• Rate Reduction of Blind Quantum Data Compression with Local Approximations Based on Unstable Structure of Quantum States
• Source Compression with a Quantum Helper
• A Rate-Distortion Perspective on Quantum State Redistribution
• Fully Quantum Source Compression with a Quantum Helper
• Information-Theoretic Limits of Quantum Learning via Data Compression