Mixed state concurrence for symmetric systems

TL;DR

This paper introduces a symmetry-based method to quantify entanglement in mixed states of symmetric quantum systems, accounting for degeneracies and providing a practical measure for small spin systems.

Contribution

The authors develop a novel approach leveraging symmetry to construct unentangled densities, enabling accurate entanglement quantification in mixed states of symmetric systems.

Findings

Method effectively quantifies entanglement in small spin systems.

Symmetry constrains entanglement reduction due to degeneracies.

Results demonstrate the approach's applicability to various symmetric models.

Abstract

We present a method to quantify entanglement in mixed states of highly symmetric systems. Symmetry constrains interactions between parts and predicts the degeneracies of the states. While symmetry alone produces entangled eigenstates, the thermal mixed state (density) which contains all of the eigenstate densities weighted by their Boltzmann factors is not necessarily as entangled as the eigenstates themselves because generally the mixed state can be re-expressed as a sum over densities which are less entangled. The entanglement of the mixed state is the minimum obtained by considering all such re-expressions, but there is no well-defined approach to solving this problem generally. Our method uses symmetry to explicitly construct unentangled densities, which are then optimally included in the thermal mixed state, resulting in a quantitative measure of entanglement that accounts for the reduction of entanglement arising from degenerate states. We present results for several small spin systems.