Quantum detailed balance via elementary transitions

Abstract

Quantum detailed balance is formulated in terms of elementary transitions, in close analogy to detailed balance in a classical Markov chain on a finite set of points. An elementary transition is taken to be a pure state of two copies of the quantum system, as a quantum analogue of an ordered pair of classical points representing a classical transition from the first to the second point. This form of quantum detailed balance is shown to be equivalent to standard quantum detailed balance with respect to a reversing operation, thus providing a new conceptual foundation for the latter. Aspects of parity in quantum detailed balance are clarified in the process. The connection with the Accardi-Cecchini dual and the KMS dual (or Petz recovery map) is also elucidated.

v1: 34 pages. v2: Minor corrections, changes and additions. Further references. 35 pages. v3: New Section 2 added. Additional minor corrections, changes and references. Journal style. 34 pages