Universal recoverability of quantum states in tracial von-Neumann algebras

TL;DR

This paper extends the quantum data processing inequality to tracial von-Neumann algebras, establishing a universal recoverability bound using the Petz recovery map that was previously known only in finite dimensions.

Contribution

It generalizes the quantum recoverability results from finite-dimensional systems to infinite-dimensional tracial von-Neumann algebras.

Findings

Established a universal recoverability bound in infinite-dimensional setting.

Extended the quantum data processing inequality for sandwiched quasi-relative entropy.

Demonstrated the applicability of Petz recovery map in broader algebraic contexts.

Abstract

In this paper, we discuss a refinement of quantum data processing inequality for the sandwiched quasi-relative entropy $\mathcal{S}_2$ on a tracial von-Neumann algebra. The main result is a universal recoverability bound with the Petz recovery map, which was previously obtained in the finite dimensional setup.