2007/05/08 by Mari Carmen Bañuls, Mari-Carmen Bañuls, J. I. Cirac +2 · 2 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum many-body systems #quant-ph
paper · pdf · doi:10.1103/physreva.76.022311
published as Physical Review A 76, 022311 (2007) · 13 pages, 3 figures, 4 tables
arxiv created 2007/05/08 · openalex publication_date 2007/08/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The anticommuting properties of fermionic operators, together with the presence of parity conservation, affect the concept of entanglement in a composite fermionic system. Hence different points of view can give rise to different reasonable definitions of separable and entangled states. Here we analyze these possibilities and the relationship between the different classes of separable states. The behavior of the various classes when taking multiple copies of a state is also studied, showing that some of the differences vanish in the asymptotic regime. In particular, in the case of only two fermionic modes all the classes become equivalent in this limit. We illustrate the differences and relations by providing a complete characterization of all the sets defined for systems of two fermionic modes. The results are applied to Gibbs states of infinite chains of fermions whose interaction corresponds to a XY Hamiltonian with transverse magnetic field.