Universal methods for extending any entanglement witness from the bipartite to the multipartite case

Abstract

Any bipartite entanglement witness $W$ can be written as $W=c_{\sigma }I-\sigma$, where $\sigma$ is a quantum state, $I$ is the identity matrix, and $c_{\sigma }$ is a non-negative number. We present a general method to extend the given entanglement witness to multipartite cases via purification, partial purification, and direct tensor of the quantum state $\sigma$. Our methods extend $\sigma$ but leave the parameter $c_{\sigma }$ untouched. This is very valuable since the parameter is generally not easy to compute.

arXiv comment7 pages, to rewrite the abstract in details

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Cited by in corpus (3)

• Entangled states in the role of witnesses
• The hierarchies of "witnesses" and the properties and characterization of entangled states as super entanglement witnesses
• Internal Boundary between Entanglement and Separability Within a Quantum State