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.

7 pages, 6 figures, Accepted for publication in Quantum Information Processing

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Cited by in corpus (13)

• Entanglement in indistinguishable particle systems
• Witnessed entanglement and the geometric measure of quantum discord
• Entanglement of indistinguishable particles as a probe for quantum phase transitions in the extended Hubbard model
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
• Computable Measures for the Entanglement of Indistinguishable Particles
• Entanglement Witnesses for Indistinguishable Particles
• Spectral properties of reduced fermionic density operators and parity superselection rule
• Quantumness of correlations in indistinguishable particles
• Quantumness of Correlations in Fermionic Systems
• Quantum correlations of identical particles subject to classical environmental noise
• Teleporting quantum information encoded in fermionic modes
• Probing the sign of on-site Hubbard interaction by two-particle quantum walks
• Completely Positive Maps for Reduced States of Indistinguishable Particles