Unextendible product bases and the construction of inseparable states

Details Unextendible product bases and the construction of inseparable states Unextendible product bases and the construction of inseparable states

2002-08-05

arxiv.org/abs/quant-ph/0208028v1

Linear Alg. Appl. 359 (2003) 235-258

Physics

Quantum Physics

to appear in Lin. Alg. Appl

Scientific paper

Let H[N] denote the tensor product of n finite dimensional Hilbert spaces H(r). A state |phi> of H[N] is separable if |phi> is the tensor product of states in the respective product spaces. An orthogonal unextendible product basis is a finite set B of separable orthonormal states |phi(k)> such that the non-empty space B9perp), the set of vectors orthogonal to B, contains no separable projection. Examples of orthogonal UPB sets were first constructed by Bennett et al [1] and other examples appear, for example, in [2] and [3]. If F denotes the set of convex combinations of the projections |phi(k)>

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