Quantifying Quantum Correlations in Fermionic Systems using Witness Operators

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.