Inertias of entanglement witnesses. (10th November 2020)

• Record Type: Journal Article
• Authors: Shen, Yi; Chen, Lin; Zhao, Li-Jun
• Is Part Of: Journal of physics. Volume 53:Number 48(2020)
• Publication Date: 2020-11-10
• Subjects: matrix inertia -- entanglement witnesses -- partial transpose of NPT state; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/abbec1
• Languages: English
• ISSNs: 1751-8113

Abstract

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.