Unextendible product bases and the construction of inseparable states

Content Provider	Semantic Scholar
Author	Pittenger, A. O.
Copyright Year	2002
Abstract	Abstract Let H ( N ) denote the tensor product of n finite dimensional Hilbert spaces H ( r ) . A state ϕ of H ( N ) is separable if ϕ = α 1 ⊗⋯⊗ α n where the states α r are in H r . An orthogonal unextendible product basis is a finite set B of separable orthonormal states ϕ k ,1⩽k⩽m such that the non-empty space B ⊥ , the set of vectors orthogonal to B , contains no separable state. Examples of orthogonal UPB sets were first constructed by Bennett et al. 1 and other examples and references appear, for example, in 3 . If F=F B denotes the set of convex combinations of ϕ k ϕ k ,1⩽k⩽m , then F is a face in the set S of separable densities. In this note we show how to use F to construct families of positive partial transform states ( PPT ) which are not separable. We also show how to make an analogous construction when the condition of orthogonality is dropped. The analysis is motivated by the geometry of the faces of the separable states and leads to a natural construction of entanglement witnesses separating the inseparable PPT states from S .
Starting Page	235
Ending Page	248
Page Count	14
File Format	PDF HTM / HTML
DOI	10.1016/S0024-3795(02)00423-8
Volume Number	359
Alternate Webpage(s)	https://arxiv.org/pdf/quant-ph/0208028v1.pdf
Alternate Webpage(s)	https://doi.org/10.1016/S0024-3795%2802%2900423-8
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article