Von Neumann Entropy-Preserving Quantum Operations

TL;DR

This paper investigates conditions under which quantum operations preserve von Neumann entropy of states and the entropy of their associated bipartite maps, providing insights into quantum decoherence and information preservation.

Contribution

It characterizes pairs of quantum operations that preserve von Neumann entropy of states and their induced bipartite map entropies, advancing understanding of entropy-preserving quantum processes.

Findings

Identifies conditions for entropy preservation in quantum states.

Characterizes pairs of operations maintaining bipartite map entropy.

Provides a framework for analyzing decoherence in quantum operations.

Abstract

For a given quantum state $\rho$ and two quantum operations $\Phi$ and $\Psi$, the information encoded in the quantum state $\rho$ is quantified by its von Neumann entropy $\S(\rho)$. By the famous Choi-Jamio{\l}kowski isomorphism, the quantum operation $\Phi$ can be transformed into a bipartite state, the von Neumann entropy $\S^{\mathrm{map}}(\Phi)$ of the bipartite state describes the decoherence induced by $\Phi$. In this Letter, we characterize not only the pairs $(\Phi, \rho)$ which satisfy $\S(\Phi(\rho))=\S(\rho)$, but also the pairs $(\Phi, \Psi)$ which satisfy $\S^{\mathrm{map}}(\Phi\circ\Psi) = \S^{\mathrm{map}}(\Psi)$.