Completely Positive Maps for Reduced States of Indistinguishable Particles

TL;DR

This paper develops a framework for constructing completely positive maps for subsystems of indistinguishable fermionic particles, addressing the challenge of correlated global states where system and environment are indistinguishable, and focusing on exchange correlations.

Contribution

It introduces a novel method to define reduced completely positive maps in fermionic systems with exchange correlations, expanding the understanding of open quantum systems with indistinguishable particles.

Findings

Reduced maps are possible for certain fermionic states with exchange correlations.

The framework handles correlated global states where system and environment are indistinguishable.

It extends the theory of quantum maps to more complex many-body systems.

Abstract

We introduce a framework for the construction of completely positive maps for subsystems of indistinguishable fermionic particles. In this scenario, the initial global state is always correlated, and it is not possible to tell system and environment apart. Nonetheless, a reduced map in the operator sum representation is possible for some sets of states where the only non-classical correlation present is exchange.