Tabletop reversibility of phase-covariant operations

Abstract

Irreversibility and time-translation symmetry are both fundamental in open quantum dynamics, and it is of great importance to study the interplay between them. In this paper, we study tabletop reversibility (TTR) for phase-covariant quantum operations and obtain sharply different conclusions for finite-dimensional and Gaussian systems. For finite-dimensional systems, we prove that any phase-covariant operation that admits a Petz recovery map can be implemented by a dilation which is both time-translational symmetric and tabletop time reversible. In contrast, for phase-covariant Gaussian operations we exhibit a concrete obstruction: any Gaussian dilation of a single-mode Gaussian amplification channel is not tabletop time reversible. As a byproduct, we find that almost every completely positive and trace preserving (CPTP) map admits a dilation that realizes TTR. These results clarify whether and how TTR can be realized under phase-covariant symmetry constraints and reveal a qualitative difference between finite-dimensional and Gaussian systems.

16 pages, 3 figures

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