Entropic entanglement criteria for Fermion systems

Abstract

Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one particle reduced density matrix, on the other one. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi's entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi's entropic parameter is investigated. The extension of these criteria to systems of N identical fermions is also considered.

Dynamics of entanglement in systems of identical fermions undergoing decoherence

“…For two-fermion states the entanglement criterion improves as α increases and is the most efficient in the limit α → ∞ [21]. Note that the criterion associated with the von Neumann entropy constitutes a special instance, corresponding to the particular value α → 1 of the Rényi entropic parameter.…”

“…On one hand, the concept of entanglement in these kinds of systems exhibits some differences from the corresponding concept as applied to systems consisting of distinguishable subsystems, being perhaps more controversial. However, there is general consensus that in systems of identical fermions the minimum quantum correlations between the particles that are required by the indistinguishability and * andreavh@if.ufrj.br, anamajtey@if.ufrj.br, arplastino@unnoba.edu.ar the antisymmetry of the fermionic state do not contribute to the state's entanglement [7,[11][12][13][14][15][16][17][18][19][20][21][22][23][24]. On the other hand, a resource theory based on local operations and classical communication (LOCCs) is no longer suitable: Due to the necessary (anti)symmetrization of identical particles' states, the notion of local operations does not apply anymore.…”

Algebraic approach to entanglement and entropy

“…That is evident from the impressive volume of inconclusive literature on fermions and bosons, and the apparent absence of any treatment of para-and braidstatistics [3][4][5][6][7][8][9][10][11][12].…”

Characterization of correlations in two-fermion systems based on measurement induced disturbances

“…It is useful to regard a system constituted by identical fermions with a single-particle Hilbert space of dimension 2k (with k ≥ 2) as a system consisting of spin-s particles, with s = (2k − 1)/2 [10,12,13]. An orthonormal basis {|i , i = 1, .…”

“…Considerable attention has recently been devoted to the applications of tools and concepts from quantum information theory to the study of correlations in systems of identical fermions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. A key role in these developments was played by the work of Ghirardi and collaborators [1,2], who advanced a clear and physically motivated formulation of the concept of separability for systems of identical particles.…”