Necessary and Sufficient Condition on the Lindblad Equation to Prevent Entropy Increase

TL;DR

This paper establishes a precise condition on Lindblad operators ensuring the von Neumann entropy never decreases, linking unitarity and Hermitian properties to entropy preservation in quantum dynamics.

Contribution

It provides a necessary and sufficient condition for Lindblad equations to prevent entropy decrease, clarifying the role of operator unitarity and Hermitian equivalence in quantum evolution.

Findings

Operators must be unitary linear combinations of their adjoints to prevent entropy decrease

Such operators can be replaced with Hermitian operators without altering the evolution

The condition is both necessary and sufficient for entropy non-decrease in Lindblad dynamics

Abstract

It is shown that in order for the solutions of the Lindblad equation never to give a decreasing von Neumann entropy, it is necessary and sufficient that the operators appearing in this equation should be unitary linear combinations of their adjoints. In this case, these operators may be replaced with Hermitian operators, without changing the evolution of density matrices.