Towards measuring Entanglement Entropies in Many Body Systems

Abstract

We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that in general, the Shannon entropy of the probability distribution of certain symmetry observables gives a lower bound to the entropy. In some cases this bound is saturated and directly gives the entropy. We also show other cases in which the probability distribution contains enough information to extract the entropy: we show how this is done in several examples including BEC wave functions, the Dicke model, XY spin chain and chains with strong randomness.

References in corpus (2)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Remote state preparation: arbitrary remote control of photon polarization

Cited by in corpus (29)

• Quantum Noise as an Entanglement Meter
• Entanglement from Charge Statistics: Exact Relations for Many-Body Systems
• Measuring entanglement using quantum quenches
• Random matrices and entanglement entropy of trapped Fermi gases
• Symmetry-resolved entanglement for excited states and two entangling intervals in AdS${}_3$/CFT${}_2$
• A note on the Full Counting Statistics of paired fermions
• Factorization of quantum charge transport for non-interacting fermions
• Protecting clean critical points by local disorder correlations
• Fluctuations and Entanglement spectrum in quantum Hall states
• Entanglement entropy in dynamic quantum-coherent conductors
• Variational thermal quantum simulation of the lattice Schwinger model
• Entanglement Entropy and Mutual Information in Bose-Einstein Condensates
• Heisenberg Uncertainty Principle as Probe of Entanglement Entropy: Application to Superradiant Quantum Phase Transitions
• Detecting entanglement of random states with an entanglement witness
• Realistic protocol to measure entanglement at finite temperatures
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Macroscopic Observables Detecting Genuine Multipartite Entanglement and Partial Inseparability in Many-Body Systems
• Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach
• Entanglement properties and ground-state statistics of free bosons
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Bipartite Fluctuations of Critical Fermi Surfaces
• Phases of the Bose-Einstein condensate dark matter model with both two- and three-particle interactions
• Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor
• Kolmogorov complexity as intrinsic entropy of a pure state: Perspective from entanglement in free fermion systems
• Characterizing Topological Order in Superconducting Systems
• Convexity of the entanglement energy of SU($2N$)-symmetric fermions with attractive interactions
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
• Variational quantum simulation of the quantum critical regime