Entanglement spectrum of mixed states

TL;DR

This paper introduces a method to analyze the entanglement spectrum of open 1D quantum systems, revealing how decoherence affects entanglement and providing practical observables for studying mixed states.

Contribution

It proposes a novel way to quantify entanglement in open quantum systems using a scaled matrix product state approach, linking entanglement spectrum to concurrence and purity.

Findings

Entanglement spectrum relates to generalized concurrence and purity.

Method applicable to single-particle evolution in open systems.

Provides accessible observables for studying 1D open quantum systems.

Abstract

Entanglement plays an important role in our ability to understand, simulate, and harness quantum many-body phenomena. In this work, we investigate the entanglement spectrum for open one-dimensional systems, and propose a natural quantifier for how much a 1D quantum state is entangled while being subject to decoherence. We demonstrate our method using a simple case of single-particle evolution and find that the open system entanglement spectrum is composed of generalized concurrence values, as well as quantifiers of the state's purity. Our proposed entanglement spectrum can be directly obtained using a correct scaling of a matrix product state decomposition of the system's density matrix. Our method thus offers new observables that are easily acquired in the study of interacting 1D systems, and sheds light on the approximations employed in matrix product state simulations of open system dynamics.