Ensemble averaged entanglement of two-particle states in Fock space

Abstract

Recent results, extending the Schmidt decomposition theorem to wavefunctions of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and to a pair of bosons in the the Bose-Hubbard model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasised.

19 pages Latex, changed title, references added in the conclusions

References in corpus (32)

• Measures and dynamics of entangled states
• Quantum Correlations in Two-Fermion Systems
• General criterion for the entanglement of two indistinguishable particles
• Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity
• The one-dimensional Hubbard model: A reminiscence
• Entanglement versus Bell violations and their behaviour under local filtering operations
• Purity of Gaussian states: measurement schemes and time-evolution in noisy channels
• Quantifying decoherence in continuous variable systems
• Efficient Generation of Generic Entanglement
• Linear entropy as an entanglement measure in two-fermion systems
• A generalized skew information and uncertainty relation
• An elementary formula for entanglement entropies of fermionic systems
• Entanglement sharing in one-particle states
• Emergence of typical entanglement in two-party random processes
• Thermodynamics and excitations of the one-dimensional Hubbard model
• Global entangling properties of the coupled kicked tops
• Entanglement dynamics of electron-electron scattering in low-dimensional semiconductor systems
• Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements
• The Bell Inequality and Entanglement
• Canonical and micro-canonical typical entanglement of continuous variable systems
• Entanglement of two delocalised electrons
• Canonical entanglement for two indistinguishable particle
• Continuous-Variable Spatial Entanglement for Bright Optical Beams
• Dynamical entanglement and chaos: the case of Rydberg molecules
• Teleportation fidelities of squeezed states from thermodynamical state space measures
• A generalized quantum microcanonical ensemble
• Criteria for the entanglement of composite systems of identical particles
• Genuine tripartite entanglement in the non-interacting Fermi gas
• Bipartite entanglement and localization of one-particle states
• Dynamics of quantum correlations and linear entropy in a multi-qubit-cavity system
• Spatial Entanglement of a Free Bosonic Field
• Entanglement of a microcanonical ensemble

Cited by in corpus (18)

• Entanglement in indistinguishable particle systems
• Effects of symmetry breaking in finite quantum systems
• Separability Criteria and Entanglement Measures for Pure States of N Identical Fermions
• Quantum entanglement in exactly soluble atomic models: The Moshinsky model with three electrons, and with two electrons in a uniform magnetic field
• Exchange Symmetry and Multipartite Entanglement
• Two-electron entanglement in elliptically deformed quantum dots
• Multipartite concurrence for identical-fermion systems
• The Relationship Between Entanglement, Energy, and Level Degeneracy in Two-Electrons Systems
• The lowest excited configuration of harmonium
• Entropic Entanglement Criteria for Fermion Systems
• Magnetic alteration of entanglement in two-electron quantum dots
• Entanglement generation through particle detection in systems of identical fermions
• Tuning spatial entanglement in interacting few-electron quantum dots
• Dynamics of entanglement in systems of identical fermions undergoing decoherence
• Entanglement transitions in random definite particle states
• Entanglement of electron pairs extracted from a many-body system
• A geometrical crossover in excited states of two-electron quantum dots in a magnetic field
• Entanglement as an indicator of a geometrical crossover in a two-electron quantum dot in a magnetic field