Entanglement, Particle Identity and the GNS Construction: A Unifying Approach
arXiv:1205.2882 · doi:10.1103/PhysRevLett.110.080503
Abstract
A novel approach to entanglement, based on the Gelfand-Naimark-Segal (GNS) construction, is introduced. It considers states as well as algebras of observables on an equal footing. The conventional approach to the emergence of mixed from pure ones based on taking partial traces is replaced by the more general notion of the restriction of a state to a subalgebra. For bipartite systems of nonidentical particles, this approach reproduces the standard results. But it also very naturally overcomes the limitations of the usual treatment of systems of identical particles. This GNS approach seems very general and can be applied for example to systems obeying para- and braid- statistics including anyons.
20 pages, 1 figure
References in corpus (21)
- Quantum entanglement
- Quantum Entanglement in Fermionic Lattices
- Quantum Correlations in Systems of Indistinguishable Particles
- Quantum Correlations in Two-Fermion Systems
- The entanglement of indistinguishable particles shared between two parties
- An Introduction to Noncommutative Spaces and their Geometry
- A subsystem-independent generalization of entanglement
- General criterion for the entanglement of two indistinguishable particles
- Quantum Correlations in Two-Boson Wavefunctions
- Essential entanglement for atomic and molecular physics
- Entanglement in a two-identical-particle system
- Quantum Entanglement of Identical Particles
- Separability Criteria and Entanglement Measures for Pure States of N Identical Fermions
- An elementary formula for entanglement entropies of fermionic systems
- A generalized skew information and uncertainty relation
- Entanglement of Indistinguishable Particles
- Useful entanglement from the Pauli principle
- Entanglement for multipartite systems of indistinguishable particles
- Entropic Entanglement Criteria for Fermion Systems
- Quantum entanglement in a non-commutative system
- Entanglement beyond tensor product structure: algebraic aspects of quantum non - separability
Cited by in corpus (79)
- Quantum enhanced measurements without entanglement
- Extracting entanglement from identical particles
- Indistinguishability of elementary systems as resource for quantum information processing
- Quantum entanglement of identical particles by standard information-theoretic notions
- Entanglement in indistinguishable particle systems
- Reasonable fermionic quantum information theories require relativity
- Algebraic Approach to Entanglement and Entropy
- Entanglement in fermion systems and quantum metrology
- Entanglement between identical particles is a useful and consistent resource
- Robust entanglement preparation against noise by controlling spatial indistinguishability
- Entanglement of indistinguishable particles as a probe for quantum phase transitions in the extended Hubbard model
- Entanglement of Identical Particles
- Entanglement in fermionic chains with finite range coupling and broken symmetries
- Quasi-pinning and entanglement in the lithium isoelectronic series
- Dealing with indistinguishable particles and their entanglement
- A path integral Monte Carlo method for Rényi entanglement entropies
- Universality of Schmidt decomposition and particle identity
- Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation
- Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
- Energetics of correlations in interacting systems
- Particle entanglement in continuum many-body systems via quantum Monte Carlo
- Measurement of Identical Particle Entanglement and the Influence of Antisymmetrisation
- Black holes as random particles: entanglement dynamics in infinite range and matrix models
- Entanglement Witnesses for Indistinguishable Particles
- Entanglement and correlation in two-nucleon systems
- Dissipative quantum metrology in manybody systems of identical particles
- Relating correlation measures: the importance of the energy gap
- Entangling Bosons through Particle Indistinguishability and Spatial Overlap
- Quantumness of correlations in indistinguishable particles
- From observables and states to Hilbert space and back: a 2-categorical adjunction
- Dynamics of spatially indistinguishable particles and entanglement protection
- Entanglement of Identical Particles and Coherence in the First Quantization Language
- Quantum information as a non-Kolmogorovian generalization of Shannon's theory
- The lowest excited configuration of harmonium
- One-body entanglement as a quantum resource in fermionic systems
- A Matrix Model for QCD
- Entanglement robustness via spatial deformation of identical particle wave functions
- Entangling three identical particles via spatial overlap
- Target space entanglement in Matrix Models
- Quantum State Reduction: Generalized Bipartitions from Algebras of Observables
- Quantumness of Correlations in Fermionic Systems
- Teleporting quantum information encoded in fermionic modes
- Many-body entanglement in fermion systems
- Entanglement in Algebraic Quantum Mechanics: Majorana fermion systems
- Indistinguishability-enhanced entanglement recovery by spatially localized operations and classical communication
- On the Möbius transformation in the entanglement entropy of fermionic chains
- Particle partition entanglement of one dimensional spinless fermions
- Transmission of quantum entanglement through a random medium
- Target space entanglement in quantum mechanics of fermions and matrices
- Non-abelian symmetry-resolved entanglement entropy
- Spatial separation and entanglement of identical particles
- Hanbury Brown-Twiss Effect with Wave Packets
- Measuring quantumness: from theory to observability in interferometric setups
- Direct measurement of particle statistical phase
- Orbital and electronic entanglement in quantum teleportation schemes
- Tunable mode entanglement: topological Su-Schrieffer-Heeger (SSH) chain with an embedded Aharonov-Bohm quantum ring
- Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator
- Codification Volume of an operator algebra and its irreversible growth through thermal processes
- Entanglement and algebraic independence in fermion systems
- Entanglement entropy and non-local duality: quantum channels and quantum algebras
- Generating indistinguishability within identical particle systems: spatial deformations as quantum resource activators
- Completely Positive Maps for Reduced States of Indistinguishable Particles
- Entanglement Witnessing for Lattice Gauge Theories
- Unifying Entanglement with Uncertainty via Symmetries of Observable Algebras
- Quantumness and the role of locality on quantum correlations
- Taming identical particles for discerning the genuine non-locality
- Entropy of Quantum States: Ambiguities
- Bipartite representations and many-body entanglement of pure states of indistinguishable particles
- Majorana Fermions and Orthogonal Complex Structures
- Disorder-free localisation in continuous-time quantum walks : Role of symmetries
- Measuring Correlation and Entanglement between Molecular Orbitals on a Trapped-Ion Quantum Computer
- Anomalies and Renormalization of Impure States in Quantum Theories
- On states of quantum theory
- Reduced density matrix of nonlocal identical particles
- A Scaling Function for the Particle Entanglement Entropy of Fermions
- Fast Scramblers, Democratic Walks and Information Fields
- Entanglement of Spatial Regions vs. Entanglement of Particles
- Entanglement in a Maxwell Theory coupled to a non-relativistic particle
- Emergent Gauge Symmetries and Quantum Operations