Correlations in local measurements and entanglement in many-body systems

Abstract

While entanglement plays an important role in characterizing quantum many-body systems, it is hardly possible to directly access many-body entanglement in real experiments. In this paper, we study how bipartite entanglement of many-body states is manifested in the correlation of local measurement outcomes. In particular, we consider a measure of correlation defined as the statistical distance between the joint probability distribution of local measurement outcomes and the product of its marginal distributions. Various bounds of this measure are obtained and several examples of many-body states are considered as a testbed for the measure. We also generalize the framework to the case of imprecise measurement and argue that the considered measure is related to the concept of quantum macroscopicity.

10 pages, 4 figures; comments welcome; correct figures

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Nonlinear atom interferometer surpasses classical precision limit
• On the quantum, classical and total amount of correlations in a quantum state
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Aspects of generic entanglement
• Macroscopic quantum states: measures, fragility and implementations
• The conditions for quantum violation of macroscopic realism
• Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality
• Measures of macroscopicity for quantum spin systems
• Quantification of Macroscopic Quantum Superpositions within Phase Space
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Failure of Local Realism Revealed by Extremely Coarse-Grained Measurements
• Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation
• Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions