Abstract
Witness operators are a central tool to detect entanglement or to distinguish among the different entanglement classes of multiparticle systems, which can be defined using stochastic local operations and classical communication (SLOCC). We show a one-to-one correspondence between general SLOCC witnesses and a class of entanglement witnesses in an extended Hilbert space. This relation can be used to derive SLOCC witnesses from criteria for full separability of quantum states; moreover, given SLOCC witnesses can be viewed as entanglement witnesses. As applications of this relation we discuss the calculation of overlaps between different SLOCC classes and the SLOCC classification in -dimensional systems.
Highlights
Entanglement is considered to be an important resource for applications in quantum information processing, making its characterization essential for the field [1, 2]
We show a one-to-one correspondence between general stochastic local operations and classical communication (SLOCC) witnesses and a class of entanglement witnesses in an extended Hilbert space
Entanglement is a resource if the parties are spatially separated and the allowed operations are restricted to local operations assisted by classical communication (LOCC)
Summary
Entanglement is considered to be an important resource for applications in quantum information processing, making its characterization essential for the field [1, 2]. For multipartite systems the classification via LOCC is, even for pure states very difficult, so one may consider a coarse grained classification This can be done using the notion of stochastic local operations assisted by classical communication (SLOCC). W = λ1 − |ψ ψ|, with λ being the maximal squared overlap between the entangled state |ψ and the set of all product states Such projector based witnesses can be used to distinguish between different SLOCC classes [30, 31]. In this paper we establish an one-to-one correspondence between general SLOCC witnesses for multipartite systems and a class of entanglement witnesses in a higherdimensional system, built by two copies of the original one
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