IFLP   13074
INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
artículos
Título:
Entanglement in fermion systems
Autor/es:
N. GIGENA; R. ROSSIGNOLI
Revista:
PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS
Editorial:
AMER PHYSICAL SOC
Referencias:
Lugar: New York; Año: 2015 vol. 92 p. 423261 - 423269
ISSN:
1050-2947
Resumen:
We analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with a fixed number parity yet not necessarily a fixed particle number. The mode entanglement between one single-particle level and its orthogonal complement is first considered, and an entanglement entropy for such a partition of a particular basis of the single-particle Hilbert space H is defined. The sum over all single-particle modes of this entropy is introduced as a measure of the total entanglement of the system with respect to the chosen basis and it is shown that its minimum over all bases of H is a function of the one-body density matrix. Furthermore, we show that if minimization is extended to all bases related through a Bogoliubov transformation, then the entanglement entropy is a function of the generalized one-body density matrix. These results are then used to quantify entanglement in fermion systems with four single-particle levels. For general pure states of such a system a closed expression for the fermionic concurrence is derived, which generalizes the Slater correlation measure defined by J. Schliemann et al. [Phys. Rev. A 64, 022303 (2001)], implying that particle entanglement may be seen as minimum mode entanglement. It is also shown that the entanglement entropy defined before is related to this concurrence by an expression analogous to that in the two-qubit case. For mixed states of this system the convex roof extension of the previous concurrence and entanglement entropy is evaluated analytically, extendingthe results in previous reference to general states.