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Low dimensional bound entanglement with one-way distillable cryptographic key

Karol Horodecki·Lukasz Pankowski·Michal Horodecki·Pawel Horodecki
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Abstract

We provide a class of bound entangled states that have positive distillable secure key rate. The smallest state of this kind is $4 \otimes 4$, which shows that peculiar security contained in bound entangled states does not need high dimensional systems. We show, that for these states a positive key rate can be obtained by {\it one-way} Devetak-Winter protocol. Subsequently the volume of bound entangled key-distillable states in arbitrary dimension is shown to be nonzero. We provide a scheme of verification of cryptographic quality of experimentally prepared state in terms of local observables. Proposed set of 7 collective settings is proven to be optimal in number of settings.

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Karol Horodecki, Lukasz Pankowski, Michal Horodecki, Pawel Horodecki. 2005-06-24. Low dimensional bound entanglement with one-way distillable cryptographic key. https://doi.org/10.1109/tit.2008.921709

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