Entanglement and Tensor Product Decomposition for Two Fermions

Abstract

The problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators is discussed. The set of physical states of the composite system is restricted by the superselection rule forbidding the superposition of fermions and bosons. It is shown that the Wootters concurrence is not proper entanglement measure in this case. The explicit formula for the entanglement of formation is found and its dependence on tensor product decompositions of the Hilbert space is discussed. It is shown that the set of separable states is narrower than in two-qubit case. Moreover, there exist states which are separable with respect to all tensor product decompositions of the Hilbert space.

8pp, published version

References in corpus (6)

• The entanglement of indistinguishable particles shared between two parties
• Quantum tensor product structures are observable-induced
• General criterion for the entanglement of two indistinguishable particles
• Entanglement constrained by superselection rules
• Quantum nonlocality in the presence of superselection rules and data hiding protocols
• Nonlocal resources in the presence of Superselection Rules

Cited by in corpus (28)

• Entanglement in fermionic systems
• Fermionic mode entanglement in quantum information
• Observer dependent entanglement
• Autonomous quantum thermal machine for generating steady-state entanglement
• Entanglement in indistinguishable particle systems
• Quantum fisher information in noninertial frames
• Reasonable fermionic quantum information theories require relativity
• The thermodynamics of creating correlations: Limitations and optimal protocols
• Fermionic entanglement ambiguity in non-inertial frames
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
• Energetics of correlations in interacting systems
• Qubit-Qutrit Separability-Probability Ratios
• Characterization of Unruh Channel in the context of Open Quantum Systems
• Comment on "Fermionic entanglement ambiguity in noninertial frames"
• Local optimization on pure Gaussian state manifolds
• Teleporting quantum information encoded in fermionic modes
• Multipartite quantum correlations in even and odd spin coherent states
• Robust fermionic-mode entanglement of a nanoelectronic system in non-Markovian environments
• Capacities of Grassmann channels
• Tripartite Entanglement-Dependence of Tripartite Non-locality in Non-inertial Frame
• Detection of Topology via Entanglement Oscillations
• Continuous frames in tensor product Hilbert spaces, localization operators and density operators
• Multipartite entanglement in fermionic systems via a geometric measure
• Nonlinear Bogolyubov-Valatin transformations and quaternions
• Maximally entangled fermions
• Nonlinear Bogolyubov-Valatin transformations: 2 modes
• Quantum Statistical Mechanics of Electronically Open Molecules: Reduced Density Operators
• Does Quantum Information Require Additional Structure?