Heat transfer operators associated with quantum operations

• Published in: Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2011-07, Vol.44 (27), p.275304-18
• Main Authors: Aksak, Ç, Turgut, S
• Format: Article
• Language: English
• Subjects: Constrictions; Equivalence; Exact sciences and technology; Heat exchange; Heat transfer; Mathematical analysis; Operators; Physics; Transformations; Transformations (mathematics)
• ISSN: 1751-8121; 1751-8113; 1751-8121
• DOI: 10.1088/1751-8113/44/27/275304

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 paper is to investigate 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 paper 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.