# Entanglement preserving local thermalization

## TL;DR

This paper demonstrates that entanglement can survive local thermalization processes involving classical correlations, providing explicit protocols and bounds, and exploring implications for thermodynamics and resource preservation.

## Contribution

It introduces protocols showing entanglement preservation during local thermalization at nonzero temperatures and analyzes their thermodynamic and resource implications.

## Key findings

- Entanglement can survive local thermalization with classical correlations.
- Explicit protocols for entanglement-preserving thermalization are provided.
- Bounds on the amount of preserved entanglement are established.

## Abstract

We investigate whether entanglement can survive the thermalization of subsystems. We present two equivalent formulations of this problem: (1) Can two isolated agents, accessing only pre-shared randomness, locally thermalize arbitrary input states while maintaining some entanglement? (2) Can thermalization with local heat baths, which may be classically correlated but do not exchange information, locally thermalize arbitrary input states while maintaining some entanglement? We answer these questions in the positive at every nonzero temperature and provide bounds on the amount of preserved entanglement. We provide explicit protocols and discuss their thermodynamic interpretation: we suggest that the underlying mechanism is a speed-up of the subsystem thermalization process. We also present extensions to multipartite systems. Our findings show that entanglement can survive locally performed thermalization processes accessing only classical correlations as a resource. They also suggest a broader study of the channel's ability to preserve resources and of the compatibility between global and local dynamics.