Maximally and minimally correlated states attainable within a closed evolving system

TL;DR

This paper investigates the limits of correlation in closed quantum systems, providing solutions for two-qubit systems and a classical optimization approach for larger systems to find maximally and minimally correlated states.

Contribution

It introduces a method to determine extremal correlation states within a closed quantum system, including energy conservation constraints, with explicit solutions for two-qubit systems.

Findings

Exact solutions for two-qubit systems

Reduction to classical optimization for larger systems

Insights into correlation bounds in quantum thermodynamics

Abstract

The amount of correlation attainable between the components of a quantum system is constrained if the system is closed. We provide some examples, largely from the field of quantum thermodynamics, where knowing the maximal possible variation in correlations is useful. The optimization problem it raises requires us to search for the maximally and minimally correlated states on a unitary orbit, with and without energy conservation. This is fully solvable for the smallest system of two qubits. For larger systems the problem is reduced to a manageable, classical optimization.