Recoverability in quantum information theory

TL;DR

This paper improves the understanding of quantum relative entropy's behavior under physical evolutions by establishing bounds that quantify the reversibility of quantum processes, with broad implications for quantum information theory.

Contribution

It introduces new bounds with remainder terms for quantum relative entropy inequalities, enabling quantification of the reversibility of quantum evolutions.

Findings

Established bounds for quantum relative entropy with recovery operations

Quantified the reversibility of quantum physical evolutions

Provided improvements to known entropy inequalities

Abstract

The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities.