One-shot lossy quantum data compression

TL;DR

This paper develops a one-shot quantum rate distortion framework to determine the minimal qubits needed for lossy quantum data compression, connecting finite blocklength results with asymptotic limits.

Contribution

It introduces a one-shot characterization of quantum rate distortion using smooth max-information and provides finite blocklength bounds for isotropic qubit sources.

Findings

Characterization of one-shot quantum rate distortion in terms of smooth max-information

Convergence of one-shot bounds to asymptotic rate distortion function

Finite blocklength bounds for isotropic qubit sources with average distortion

Abstract

We provide a framework for one-shot quantum rate distortion coding, in which the goal is to determine the minimum number of qubits required to compress quantum information as a function of the probability that the distortion incurred upon decompression exceeds some specified level. We obtain a one-shot characterization of the minimum qubit compression size for an entanglement-assisted quantum rate-distortion code in terms of the smooth max-information, a quantity previously employed in the one-shot quantum reverse Shannon theorem. Next, we show how this characterization converges to the known expression for the entanglement-assisted quantum rate distortion function for asymptotically many copies of a memoryless quantum information source. Finally, we give a tight, finite blocklength characterization for the entanglement-assisted minimum qubit compression size of a memoryless isotropic qubit source subject to an average symbol-wise distortion constraint.