Entanglement witnesses for fermionic lattices
Phys. Rev. A 112, 012419 – Published 22 July, 2025
DOI: https://doi.org/10.1103/j4pd-xrs1
Abstract
The fermionic partial transpose introduced by Shapourian et al. [Phys. Rev. B 95, 165101 (2017)] has received widespread attention. A fundamental application of the partial transpose lies in the construction of entanglement witnesses. However, it is a notable characteristic that the fermionic partial transpose does not preserve Hermiticity. Instead, the fermionic partial transpose of a fermionic state yields a pseudo-Hermitian operator with respect to the local parity operators. This suggests that the suitable version of entanglement witness criterion for fermions is pseudo-Hermitian. Inspired by this, we systematically investigate whether the pseudo-Hermitian operators with respect to the local parity operators can serve as valid entanglement witnesses for fermions. These contents encompass completeness, comparison, intersection, and optimal conditions. Our answer is positive. We have provided some reasons why such pseudo-Hermitian operators are more suitable as entanglement witnesses than the Hermitian ones. As a byproduct, we observe that pseudo-Hermitian witnesses can reveal more information about entanglement contained in fermionic states.
