Entanglement witnesses for indistinguishable particles

Abstract

We study the problem of witnessing entanglement among indistinguishable particles. For this purpose, we derive a set of equations which results in necessary and sufficient conditions for probing multipartite entanglement between arbitrary systems of bosons or fermions. The solution of these equations yields the construction of optimal entanglement witnesses for partial and full entanglement in discrete and continuous variable systems. Our approach unifies the verification of entanglement for distinguishable and indistinguishable particles. We provide general solutions for certain observables to study quantum entanglement in systems with different quantum statistics in noisy environments.

Two-particle four-point correlations in dynamically disordered tight-binding networks

“…However, we must point out that there is an ongoing debate regarding the observability or physical significance of correlations due to symmetrization [33,34]. Indeed, the issue arises because correlations of the type Ψ p,q Ψ * q,p represent superpositions of two-particle states where the only difference is the order of the particles.…”

Entanglement of indistinguishable particles as a probe for quantum phase transitions in the extended Hubbard model

“…For example, the correlations in eigenstates of a many-body Hamiltonian could be more naturally described by entanglement of particles, whereas certain quantum information protocols could prompt a description in terms of entanglement of modes. Once one has opted for a certain notion of entanglement, there are interesting methods to quantify it [4][5][6][31][32][33][34].…”

Multipartite concurrence for identical-fermion systems

“…For systems of identical particles, fermions or bosons, however, even the very notion of entanglement is controversial [4]. In the fermionic case, there exists some extended consensus that a pure fermion state is separable if it is a single antisymmetric product state given by a single Slater determinant [5][6][7][8][9][10][11]. In this paper we adopt such a point of view and consider entanglement in systems of identical fermions, meaning entanglement between particles and not entanglement between modes [12].…”