Inertias of entanglement witnesses

Abstract

Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We study the inertias of EWs, i.e., the triplet of the numbers of negative, zero, and positive eigenvalues respectively. We focus on the EWs constructed by the partial transposition of states with non-positive partial transposes. We provide a method to generate more inertias from a given inertia by the relevance between inertias. Based on that we exhaust all the inertias for EWs in each qubit-qudit system. We apply our results to propose a separability criterion in terms of the rank of the partial transpose of state. We also connect our results to tripartite genuinely entangled states and the classification of states with non-positive partial transposes. Additionally, the inertias of EWs constructed by X-states are clarified.

similar to the accepted version, to appear in the journal of physics a

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Cited by in corpus (5)

• A characterization of entangled two-qubit states via partial-transpose-moments
• Visualization of all two-qubit states via partial-transpose-moments
• The detection power of real entanglement witnesses under local unitary equivalence
• Constructing unextendible product bases from multiqubit ones
• Spectral characterizations of entanglement witnesses