Davies maps for qubits and qutrits

TL;DR

This paper characterizes Davies maps for qubits and qutrits, which are quantum operations preserving equilibrium states and satisfying detailed balance, providing insights into their structure and entropy properties.

Contribution

It offers a complete characterization of Davies maps for qubits and extends the analysis to qutrits, including their structure and entropy minimization.

Findings

Complete set of qubit Davies maps characterized

Minimum output entropy of Davies maps analyzed

Extension of Davies maps characterization to qutrits

Abstract

We investigate the dynamics of an N -level quantum system weakly coupled to a thermal reservoir. For any fixed temperature of the bath there exists a natural reference state: the equilibrium state of the system. Among all quantum operations on the system one distinguishes Davies maps, they pre- serve the equilibrium state, satisfy the detailed balance condition and belong to a semi-group. A complete characterization of the three dimensional set of qubit Davies maps is given. We analyze these maps and find their mini- mum output entropy. A characterization of Davies maps for qutrits is also provided.