Infinite Dimensional Choi-Jamiolkowski States and Time Reversed Quantum Markov Semigroups

TL;DR

This paper extends the Choi-Jamiolkowski state framework to infinite dimensions and introduces a new notion of time reversal for quantum Markov semigroups, measuring symmetry breaking via relative entropy.

Contribution

It defines infinite dimensional Choi-Jamiolkowski states and introduces Theta-KMS adjoint, linking time reversal and symmetry breaking in quantum Markov semigroups.

Findings

Defined infinite dimensional Choi-Jamiolkowski states.

Introduced Theta-KMS adjoint as time reversed semigroup.

Quantified symmetry breaking using von Neumann relative entropy.

Abstract

We propose a definition of infinite dimensional Choi-Jamiolkowski state associated with a completely positive trace preserving map. We introduce the notion of Theta-KMS adjoint of a quantum Markov semigroup, which is identified with the time reversed semigroup. The break down of Theta-KMS symmetry (or Theta-standard quantum detailed balance in the sense of Fagnola-Umanita) is measured by means of the von Neumann relative entropy of the Choi-Jamiolkowski states associated with the semigroup and its Theta-KMS adjoint.