Measuring Entanglement in Condensed Matter Systems

Abstract

We show how entanglement may be quantified in spin and cold atom many-body systems using standard experimental techniques only. The scheme requires no assumptions on the state in the laboratory, and a lower bound to the entanglement can be read off directly from the scattering cross section of neutrons deflected from solid state samples or the time-of-flight distribution of cold atoms in optical lattices, respectively. This removes a major obstacle which so far has prevented the direct and quantitative experimental study of genuine quantum correlations in many-body systems: The need for a full characterization of the state to quantify the entanglement contained in it. Instead, the scheme presented here relies solely on global measurements that are routinely performed and is versatile enough to accommodate systems and measurements different from the ones we exemplify in this work.

Bipartite fluctuations as a probe of many-body entanglement

“…Fluctuations at finite temperature can be compared to the Curie constant of the uniform susceptibility, 37) where the uniform susceptibility is defined as usual by…”

“…The special role played by the area of this boundary has long been recognized, and indeed was an early motivation for the study of entanglement entropy [35,36], because most Hamiltonians of interest contain local interactions which in turn lead to correlations localized along the entire boundary. In many situations this is formalized in area laws for the entanglement entropy [37], while important violations have been studied since then [8,12,38]. The important role played by the boundary, moreover, is not unique to entanglement entropy-all proposed measures of many-body entanglement are based on it.…”

“…[44]; a method for determining the lower bound is proposed in Ref. [37]; see Ref. [45] for a completely different, promising approach).…”

Probing entanglement in adiabatic quantum optimization with trapped ions

“…This constitutes a generalization of the witnesses introduced in Krammer et al [57], Cramer et al [58], De Chiara and Sanpera [59], Hauke et al [60]. Going beyond Hauke et al [60], we analyze here the "optimal" witness, obtained by minimizing W f over all f .…”

“…The above entanglement witness gives a lower bound on the best separable approximation (BSA) [58], an entanglement measure that is applicable also to mixed states. The ease of measuring this witness, both in theory and experiments, may make it an important entanglement quantifier, especially for large systems.…”