Coherence, entanglement and quantumness in closed and open systems with conserved charge, with an application to many-body localisation

TL;DR

This paper establishes a direct link between quantum coherence and entanglement in systems with conserved charge, providing practical bounds and methods to detect many-body localization and quantum phases without full state tomography.

Contribution

It introduces a novel approach to quantify and witness multipartite and bipartite entanglement through coherence and asymmetry in systems with fixed charge, applicable to open and closed quantum systems.

Findings

Quantum coherence can faithfully witness multipartite entanglement.

Bounds on entanglement are expressed as closed formulas in terms of coherence.

Method detects breaking of entanglement area law in 1D systems.

Abstract

While the scaling of entanglement in a quantum system can be used to distinguish many-body quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum systems, while measuring entanglement experimentally, even for the closed systems, requires in general quantum state tomography. In this work we show how to remedy this situation in system with a fixed or conserved charge, e.g., density or magnetization, due to an emerging relation between quantum correlations and coherence. First, we show how, in these cases, the presence of multipartite entanglement or quantumness can be faithfully witnessed simply by detecting coherence in the quantum system, while bipartite entanglement or bipartite quantum discord are implied by asymmetry (block coherence) in the system. Second, we prove that the relation between quantum correlations and coherence is also quantitative. Namely, we establish upper and lower bounds on the amount of multipartite and bipartite entanglement in a many-body system with a fixed local charge, in terms of the amount of coherence and asymmetry present in the system. Importantly, both for pure and mixed quantum states, these bounds are expressed as closed formulas, and furthermore, for bipartite entanglement, are experimentally accessible by means of the multiple quantum coherence spectra. In particular, in one-dimensional systems, our bounds may detect breaking of the area law of entanglement entropy. We illustrate our results on the example of a many-body localized system, also in the presence of dephasing.