Rényi generalization of the operational entanglement entropy

Abstract

Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] introduced an operational measure of the von Neumann entanglement entropy. Motivated by advances in measuring Rényi entropies in quantum many-body systems subject to conservation laws, we derive a generalization of the operational entanglement that is both computationally and experimentally accessible. Using the Widom theorem, we investigate its scaling with the size of a spatial subregion for free fermions and find a logarithmically violated area law scaling, similar to the spatial entanglement entropy, with at most, a double-log leading-order correction. A modification of the correlation matrix method confirms our findings in systems of up to $10^5$ particles.

Main text: 6 pages, 3 figures + Supplementary material: 6 pages

References in corpus (40)

• Entanglement Entropy and Quantum Field Theory
• Scalable multi-particle entanglement of trapped ions
• Measuring entanglement entropy through the interference of quantum many-body twins
• Quantum thermalization through entanglement in an isolated many-body system
• Calculation of reduced density matrices from correlation functions
• Reduced density matrices and entanglement entropy in free lattice models
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Quantum information can be negative
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Entanglement spectrum in one-dimensional systems
• The entanglement of indistinguishable particles shared between two parties
• Quantum tensor product structures are observable-induced
• Limits for entanglement measures
• A subsystem-independent generalization of entanglement
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Symmetry-resolved entanglement in many-body systems
• Exponential decreasing rate of leaked information in universal random privacy amplification
• Entanglement in solvable many-particle models
• General Relation between Entanglement and Fluctuations in One Dimension
• Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
• Measurement Protocol for the Entanglement Spectrum of Cold Atoms
• Entanglement constrained by superselection rules
• Nonlocal resources in the presence of Superselection Rules
• On the reduced density matrix for a chain of free electrons
• Scaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof
• Measuring entanglement in condensed matter systems
• Entanglement in fermion systems and quantum metrology
• Analytical results for the entanglement Hamiltonian of a free-fermion chain
• Sub-shot-noise quantum metrology with entangled identical particles
• Renyi Entropy of the Interacting Fermi Liquid
• Natural Entanglement in Bose-Einstein Condensates
• Free-fermion entanglement and spheroidal functions
• A path integral Monte Carlo method for Rényi entanglement entropies
• Wiener-Hopf operators in higher dimensions: the Widom conjecture for piece-wise smooth domains
• A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions
• Entanglement of identical particles and reference phase uncertainty
• Entanglement Entropy and Mutual Information in Bose-Einstein Condensates
• Scaling of entanglement entropy and superselection rules
• Entangling qubit registers via many-body states of ultracold atoms

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