Detailed balance as a quantum-group symmetry of Kraus operators

TL;DR

This paper explores how detailed balance in quantum channels relates to quantum-group symmetries of Kraus operators, revealing a deep algebraic structure linked to compact quantum groups.

Contribution

It establishes a novel connection between detailed balance conditions and quantum-group symmetries of Kraus operators in quantum channels.

Findings

Detailed balance corresponds to algebraic relations of Kraus operators.

Kraus operators satisfy relations linked to compact quantum groups.

The symmetry influences the structure of quantum channels and their states.

Abstract

A unital completely positive map governing the time evolution of a quantum system is usually called a quantum channel, and it can be represented by a tuple of operators which are then referred to as the Kraus operators of the channel. We look at states of the system whose correlations with respect to the channel have a certain symmetry. Then we show that detailed balance holds if the Kraus operators satisfy a very interesting algebraic relation which plays an important role in the representation theory of any compact quantum group.