Constructing entanglement witnesses for infinite-dimensional systems

Abstract

It is shown that, every entangled state in an infinite-dimensional composite system has a simple entanglement witness of the form $\alpha I+T$ with $\alpha$ a nonnegative number and $T$ a finite rank self-adjoint operator. We also provide two methods of constructing entanglement witness and apply them to obtain some entangled states that cannot be detected by the PPT criterion and the realignment criterion.

15 pages

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• Continuous-variable quantum state designs: theory and applications
• Measurement-induced nonlocality over two-sided projective measurements
• Entanglement detection beyond the CCNR criterion for infinite-dimensions
• Detection of mixed bipartite entangled state in arbitrary dimension via structural physical approximation of partial transposition
• Implementable Hybrid Entanglement Witness
• Constructing all entanglement witnesses from density matrices
• The RCCN criterion of separability for states in infinite-dimensional quantum systems
• Optimality of a class of entanglement witnesses for $3\otimes 3$ systems
• Witness based nonlinear detection of quantum entanglement
• Constructing separable states in infinite-dimensional systems by operator matrices