Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 59, Issue 10, Pages 6755-6773Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2013.2271772
Keywords
Entanglement of purification; isotropic qubit source; quantum rate-distortion; quantum reverse Shannon theorem; quantum side information (QSI)
Funding
- Centre de Recherches Mathematiques, University of Montreal
- University of Technology Sydney (UTS)
- National Natural Science Foundation of China [61179030]
- Australian Research Council [DP120103776]
- European Commission
- ERC
- Royal Society
- Philip Leverhulme Prize
- Singapore Ministry of Education
- National Research Foundation as part of the Research Centres of Excellence programme
- ICREA Funding Source: Custom
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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.
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