Quantum rate-distortion coding with auxiliary resources

Mark M. Wilde, Nilanjana Datta, Min Hsiu Hsieh, Andreas Winter

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.

Original languageEnglish
Article number6553271
Pages (from-to)6755-6773
Number of pages19
JournalIEEE Transactions on Information Theory
Issue number10
StatePublished - 2013
Externally publishedYes


  • Entanglement of purification
  • isotropic qubit source
  • quantum rate-distortion
  • quantum reverse Shannon theorem
  • quantum side information (QSI)


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