Quantum detailed balance via elementary transitions

TL;DR

This paper introduces a new formulation of quantum detailed balance using elementary transitions, linking it to classical concepts and clarifying its relation to existing quantum dualities and parity considerations.

Contribution

It presents a novel elementary transition-based formulation of quantum detailed balance, connecting it to classical Markov chains and standard quantum detailed balance.

Findings

Equivalent to standard quantum detailed balance with respect to a reversing operation

Clarifies the role of parity in quantum detailed balance

Elucidates connections with Accardi-Cecchini dual and KMS dual maps

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.