Detecting three-qubit bound MUB diagonal entangled states via Nonlinear optimal entanglement witnesses

Abstract

One of the important approaches to detect quantum entanglement is using linear entanglement witnesses EWs. In this paper, by determining the envelope of the boundary hyper-planes defined by a family of linear EWs, a set of powerful nonlinear optimal EWs is manipulated. These EWs enable us to detect some three qubits bound MUB (mutually unbiased bases) diagonal entangled states, i.e., the PPT (positive partial transpose) entangled states. Also, in some particular cases, the introduced nonlinear optimal EWs are powerful enough to separate the bound entangled regions from the separable ones. Finally, we present numerical examples to demonstrate the practical accessibility of this approach. Keywords :nonlinear optimal entanglement witnesses, mutually unbiased bases, MUB diagonal states

34 pages 11 figures

References in corpus (26)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Experimental quantum teleportation
• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolski-Rosen Channels
• Separability criterion and inseparable mixed states with positive partial transposition
• Bell Inequalities and the Separability Criterion
• Classification of mixed three-qubit states
• A complete family of separability criteria
• Substituting Quantum Entanglement for Communication
• Mutually unbiased binary observable sets on N qubits
• Mubs and Hadamards of Order Six
• On the structure of the sets of mutually unbiased bases for N qubits
• Mutually unbiased phase states, phase uncertainties, and Gauss sums
• Bell states diagonal entanglement witnesses
• Manipulating Multi-qudit Entanglement Witnesses by Using Linear Programming
• Local transformation of mixed states of two qubits to Bell diagonal states
• Iterations of nonlinear entanglement witnesses
• Bell-states diagonal entanglement witnesses for relativistic and non-relativistic multispinor systems in arbitrary dimensions
• Generalized qudit Choi maps
• MUBs, polytopes, and finite geometries
• Multi-qubit stabilizer and cluster entanglement witnesses
• Investigating a Class of $2\otimes 2\otimes d$ Chessboard Density Matrices via Linear and Non-linear Entanglement Witnesses Constructed by Exact Convex Optimization
• Channel Estimation with Noisy Entanglement
• MUBs: From finite projective geometry to quantum phase enciphering

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• Relativistic entanglement in single-particle quantum states using Non-Linear entanglement witnesses
• Measurement-device-independent nonlinear entanglement witnesses
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• Using linear and nonlinear entanglement witnesses to generate and detect bound entangled states on an IBM quantum processor