Heat Transfer Operators Associated with Quantum Operations

TL;DR

This paper investigates the heat transfer operators (HTOs) linked to quantum operations, exploring their restrictions imposed by unitarity and thermodynamics, especially in the context of Landauer's principle and quantum erasure.

Contribution

It provides a comprehensive analysis of the restrictions on HTOs associated with quantum operations, extending understanding beyond the generalized Landauer erasure principle.

Findings

HTOs depend on the initial system state and realization details.

Restrictions on HTOs are stronger than those from entropic principles alone.

Additional constraints on HTOs exist for generic quantum operations.

Abstract

Any quantum operation applied on a physical system is performed as a unitary transformation on a larger extended system. If the extension used is a heat bath in thermal equilibrium, the concomitant change in the state of the bath necessarily implies a heat exchange with it. The dependence of the average heat transferred to the bath on the initial state of the system can then be found from the expectation value of a hermitian operator, which is named as the heat transfer operator (HTO). The purpose of this article is the investigation of the relation between the HTOs and the associated quantum operations. Since, any given quantum operation on a system can be realized by different baths and unitaries, many different HTOs are possible for each quantum operation. On the other hand, there are also strong restrictions on the HTOs which arise from the unitarity of the transformations. The most important of these is the Landauer erasure principle. This article is concerned with the question of finding a complete set of restrictions on the HTOs that are associated with a given quantum operation. An answer to this question has been found only for a subset of quantum operations. For erasure operations, these characterizations are equivalent to the generalized Landauer erasure principle. For the case of generic quantum operations however, it appears that the HTOs obey further restrictions which cannot be obtained from the entropic restrictions of the generalized Landauer erasure principle.