Entanglement in fermion systems

GIGENA, NICOLÁS ALEJANDRO; DI TULLIO, MARCO; ROSSIGNOLI, RAÚL DANTE

Al Hoceima

Workshop; School and Workshop on Quantum Information Theory and Thermodynamics at the Nanoscale; 2020

ICTP

Extending the notion of entanglement to systems of indistinguishable fermions is not a straightforward task, because indistinguishability prevents us from acting locally on the components of the system. While different approaches have been considered in studying entanglement in systems of indistinguishable particles, the notion of mode entanglement has prevailed as that which is useful because it enables a direct connection with the local operations and quantum communication (LOCC) paradigm, which makes of entanglement a quantum resource. In this talk, instead, I'll try to make a case for identifying entanglement in this systems with correlations beyond symmetrization, which can be quantified by the mixedness of the eigenvalues of the single-particle density matrix (SPDM) of the system. I'll show that there is a class of operations on the Fock space of a N-fermion system that do not increase this entanglement, and therefore that it constitutes a quantum resource.