Quantum rate distortion coding with auxiliary resources

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 i...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Wilde, Mark M, Datta, Nilanjana, Hsieh, Min-Hsiu, Winter, Andreas
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 26.06.2013
Subjects:
Cameras
Coding
Data compression
Digital audio tape
Distortion
Mathematical analysis
Quantum entanglement
Qubits (quantum computing)
Shannon theorem
Tensors
ISSN:2331-8422
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1212.5316