Coherence, entanglement and quantumness in closed and open systems with conserved charge, with an application to manybody localisation
Abstract
While the scaling of entanglement in a quantum system can be used to distinguish manybody 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 manybody 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 onedimensional systems, our bounds may detect breaking of the area law of entanglement entropy. We illustrate our results on the example of a manybody localized system, also in the presence of dephasing.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1805.00079
 Bibcode:
 2018arXiv180500079M
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Quantum Gases;
 Quantum Physics
 EPrint:
 32 pages, 12 figures, improved presentation, added references