Efficient separation of quantum from classical correlations for mixed states with a fixed charge

TL;DR

This paper introduces a method to efficiently quantify quantum correlations, including entanglement, in mixed states of open quantum systems with fixed charge, using the operator space entanglement spectrum and tensor networks.

Contribution

It presents the concept of configuration coherence as a new measure for quantum correlations in mixed states with fixed charge, and proves its validity under certain quantum evolutions.

Findings

Configuration coherence quantifies cross-boundary quantum coherence.

The measure is efficiently computable via tensor network methods.

Applicable to systems with dephasing and other Lindblad-type dynamics.

Abstract

Entanglement is the key resource for quantum technologies and is at the root of exciting many-body phenomena. However, quantifying the entanglement between two parts of a real-world quantum system is challenging when it interacts with its environment, as the latter mixes cross-boundary classical with quantum correlations. Here, we efficiently quantify quantum correlations in such realistic open systems using the operator space entanglement spectrum of a mixed state. If the system possesses a fixed charge, we show that a subset of the spectral values encode coherence between different cross-boundary charge configurations. The sum over these values, which we call "configuration coherence", can be used as a quantifier for cross-boundary coherence. Crucially, we prove that for purity non-increasing maps, e.g., Lindblad-type evolutions with Hermitian jump operators, the configuration coherence is an entanglement measure. Moreover, it can be efficiently computed using a tensor network representation of the state's density matrix. We showcase the configuration coherence for spinless particles moving on a chain in presence of dephasing. Our approach can quantify coherence and entanglement in a broad range of systems and motivates efficient entanglement detection.