A Rate-Distortion Perspective on Quantum State Redistribution

• URL: http://arxiv.org/abs/2112.11952v1
• Date: Wed, 22 Dec 2021 15:19:58 GMT
• Title: A Rate-Distortion Perspective on Quantum State Redistribution
• Authors: Zahra Baghali Khanian and Andreas Winter
• Abstract summary: We consider a rate-distortion version of the quantum state redistribution task, where the error of the decoded state is judged via an additive distortion measure. We derive a single-letter formula for the rate-distortion function of compression schemes assisted by free entanglement.
• Score: 3.04585143845864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a rate-distortion version of the quantum state redistribution task, where the error of the decoded state is judged via an additive distortion measure; it thus constitutes a quantum generalisation of the classical Wyner-Ziv problem. The quantum source is described by a tripartite pure state shared between Alice ($A$, encoder), Bob ($B$, decoder) and a reference ($R$). Both Alice and Bob are required to output a system ($\widetilde{A}$ and $\widetilde{B}$, respectively), and the distortion measure is encoded in an observable on $\widetilde{A}\widetilde{B}R$. It includes as special cases most quantum rate-distortion problems considered in the past, and in particular quantum data compression with the fidelity measured per copy; furthermore, it generalises the well-known state merging and quantum state redistribution tasks for a pure state source, with per-copy fidelity, and a variant recently considered by us, where the source is an ensemble of pure states [1], [2]. We derive a single-letter formula for the rate-distortion function of compression schemes assisted by free entanglement. A peculiarity of the formula is that in general it requires optimisation over an unbounded auxiliary register, so the rate-distortion function is not readily computable from our result, and there is a continuity issue at zero distortion. However, we show how to overcome these difficulties in certain situations.

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