A Rate-Distortion Perspective on Quantum State Redistribution
Year: 2024
Type: article
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 (ÃandB̃, respectively), and the distortion measure is encoded in an observable onÃB̃R. 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 [ZBK & AW, Proc. ISIT 2020, pp. 1858-1863 and ZBK, PhD thesis, UAB 2020, arXiv:2012.14143]. 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.
Authors: Zahra Baghali Khanian, Andreas Winter
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,495
OpenAlex ID: W4405304254