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Entanglement Theory Quantum Correlations

Three-by-three bound entanglement with general unextendible product bases

arXiv
Authors: Łukasz Skowronek

Year

2011

Paper ID

8827

Status

Preprint

Abstract Read

~2 min

Abstract Words

113

Citations

N/A

Abstract

We discuss the subject of Unextendible Product Bases with the orthogonality condition dropped and we prove that the lowest rank non-separable positive-partial-transpose states, i.e. states of rank 4 in 3 x 3 systems are always locally equivalent to a projection onto the orthogonal complement of a linear subspace spanned by an orthogonal Unextendible Product Basis. The product vectors in the kernels of the states belong to a non-zero measure subset of all general Unextendible Product Bases, nevertheless they can always be locally transformed to the orthogonal form. This fully confirms the surprising numerical results recently reported by Leinaas et al. Parts of the paper rely heavily on the use of Bezout's Theorem from algebraic geometry.

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  • We discuss the subject of Unextendible Product Bases with the orthogonality condition dropped and we prove that the lowest rank non-separable positive-partial-transpose states...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1105.2709 [2] arXiv https://arxiv.org/abs/1105.2709 [3] Publisher https://arxiv.org/abs/1105.2709

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