Constructing Entanglement Witness Via Real Skew-Symmetric Operators

Abstract

In this work, new types of EWs are introduced. They are constructed by using real skew-symmetric operators defined on a single party subsystem of a bipartite dxd system and a maximal entangled state in that system. A canonical form for these witnesses is proposed which is called canonical EW in corresponding to canonical real skew-symmetric operator. Also for each possible partition of the canonical real skew-symmetric operator corresponding EW is obtained. The method used for dxd case is extended to d1xd2 systems. It is shown that there exist Cd2xd1 distinct possibilities to construct EWs for a given d1xd2 Hilbert space. The optimality and nd-optimality problem is studied for each type of EWs. In each step, a large class of quantum PPT states is introduced. It is shown that among them there exist entangled PPT states which are detected by the constructed witnesses. Also the idea of canonical EWs is extended to obtain other EWs with greater PPT entanglement detection power.

40 pages

References in corpus (11)

• A complete family of separability criteria
• Optimal entanglement criterion for mixed quantum states
• Entanglement Detection by Local Orthogonal Observables
• Geometric entanglement witnesses and bound entanglement
• Detecting two-party quantum correlations in quantum key distribution protocols
• Bell states diagonal entanglement witnesses
• Manipulating Multi-qudit Entanglement Witnesses by Using Linear Programming
• Bell-states diagonal entanglement witnesses for relativistic and non-relativistic multispinor systems in arbitrary dimensions
• Generalized qudit Choi maps
• Multi-qubit stabilizer and cluster entanglement witnesses
• Two-qutrit Entanglement Witnesses and Gell-Mann Matrices

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