Generators of Detailed Balance Quantum Markov Semigroups
Franco Fagnola, Veronica Umanita

TL;DR
This paper characterizes when the adjoint of a quantum Markov semigroup, with respect to certain scalar products, also forms a quantum Markov semigroup satisfying detailed balance, using the Lindblad generator operators.
Contribution
It provides a complete characterization of adjoint semigroups that are quantum Markov semigroups with detailed balance, in terms of Lindblad operators and scalar products.
Findings
Characterization of adjoint semigroups as quantum Markov semigroups.
Conditions for detailed balance in terms of Lindblad operators.
Analysis of adjoints with respect to different scalar products.
Abstract
For a quantum Markov semigroup on the algebra with a faithful invariant state , we can define an adjoint with respect to the scalar product determined by . In this paper, we solve the open problems of characterising adjoints that are also a quantum Markov semigroup and satisfy the detailed balance condition in terms of the operators in the Gorini Kossakowski Sudarshan Lindblad representation of the generator of . We study the adjoint semigroup with respect to both scalar products and .
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