Ensemble-averaged entanglement of two-particle states in Fock space

Abstract

Recent results, extending the Schmidt decomposition theorem to wavefunctions of pairs 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 Bose-Hubbard model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasised.

Multipartite concurrence for identical-fermion systems

“…As stated above, this holds for any pure state of arbitrary dimensions (qubits, qudits, distinguishable, indistinguishable, fermions, bosons, etc). In particular, the usual concurrence (1), or the fermionic concurrence (13), admits an expression in terms of an observable.…”

“…Several efforts have been devoted to the study of the entanglement features in systems of N identical fermions in the last few years [13][14][15][16][17][18][19][20][21][22]. Various bipartite entanglement measures for pure N -fermion states have been discussed, yet these measures are, in general (for N > 2), difficult to implement [5].…”

Entanglement and the speed of evolution of two interacting qubits

“…The linear entropy of the marginal density matrix of a subsystem has been recently used by several researchers as a convenient entanglement measure for pure states of bipartite quantum systems (see, for instance [36]). …”

Uncertainty relations and entanglement in fermion systems

“…However, there is by now a general agreement among researchers working in this field that in systems of two or more identical fermions quantum correlations between the particles that are solely due to the antisymmetric character of the fermionic state do not contribute to the state's amount of entanglement [8][9][10][11]. For instance, an N -fermion pure state of Slater rank equal to one (that is, a state whose wave function can be represented as a single Slater determinant) has to be regarded as non-entangled [11].…”

“…The characterization of the entanglement features of systems of identical fermions constitutes a subject that is currently attracting the attention of several researchers. For example, the entanglement between pairs of electrons in a conducting band [8], the entanglement features exhibited by the eigenstates of a soluble two-electrons model atom [12], the entanglement dynamics in scattering processes involving two electrons [13], the different families of entangled states in systems of three fermions [14], and the role of entanglement in time-optimal evolutions of fermionic systems [15,16] is known only for systems with a single-particle Hilbert space of dimension 4, which is the fermionic case of smallest dimensionality admitting the phenomenon of entanglement [10] (these systems can be mapped into systems of spin-3/2 particles). There is a need for separability criteria and entanglement indicators that are relatively easy to implement in practice and which can be extended to higher dimensional two-fermion systems or to situations involving more than two fermions [17].…”