Quantifying Quantum Correlations in Fermionic Systems using Witness Operators

TL;DR

This paper introduces a method to quantify quantum correlations in fermionic systems using witness operators and semidefinite programming, extending measures like entanglement and discord to indistinguishable fermions.

Contribution

It develops a novel framework employing witness operators and SDPs to quantify quantum correlations in fermionic systems, including extensions of entanglement and discord measures.

Findings

Optimal witnesses can be efficiently computed via SDPs.

The proposed entanglement measure aligns with Schliemann concurrence for pure states.

Quantum discord acts as an upper bound for entanglement in these systems.

Abstract

We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entan- glement witness of a state with a class of problems known as semidefinite programs (SDPs), which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robust- ness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann con- currence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entanglement.