The thermodynamics of creating correlations: Limitations and optimal protocols

TL;DR

This paper explores the fundamental limits of converting energy into correlations and entanglement in quantum systems, establishing bounds, optimal protocols, and analyzing different particle types under thermodynamic constraints.

Contribution

It provides the first rigorous bounds on energy-to-correlation conversion, constructs protocols that saturate these bounds, and compares entanglement generation for fermions and bosons.

Findings

Correlations increase linearly with available energy up to a certain point.

Optimal protocols for entanglement creation are identified for fermionic modes.

Gaussian operations are near-optimal for high-energy entanglement in bosonic modes.

Abstract

We establish a rigorous connection between fundamental resource theories at the quantum scale. Correlations and entanglement constitute indispensable resources for numerous quantum information tasks. However, their establishment comes at the cost of energy, the resource of thermodynamics, and is limited by the initial entropy. Here, the optimal conversion of energy into correlations is investigated. Assuming the presence of a thermal bath, we establish general bounds for arbitrary systems and construct a protocol saturating them. The amount of correlations, quantified by the mutual information, can increase at most linearly with the available energy, and we determine where the linear regime breaks down. We further consider the generation of genuine quantum correlations, focusing on the fundamental constituents of our universe: fermions and bosons. For fermionic modes, we find the optimal entangling protocol. For bosonic modes, we show that while Gaussian operations can be outperformed in creating entanglement, their performance is optimal for high energies.