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arXiv:quant-ph/0205063 · Physics Letters A

Generic incomparability of infinite-dimensional entangled states

Rob Clifton, Brian Hepburn, Christian Wüthrich

Published Oct 1, 2002• 3 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(02)01228-8

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It is shown that the order property of pure bipartite states under stochastic local operations and classical communications (SLOCC) changes radically when dimensionality shifts from finite to infinite. In contrast to finite-dimensional systems where there is no pure incomparable state, the existence of infinitely many mutually SLOCC incomparable states is shown for infinite-dimensional systems even under the bounded energy and finite information exchange condition. These results show that the effect of the infinite dimensionality of Hilbert space, the ``infinite workspace'' property, remains even in physically relevant infinite-dimensional systems.