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Low-Dimensional Bound Entanglement With One-Way Distillable Cryptographic Key

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4 Author(s)
Horodecki, K. ; Inst. of Comput. Sci., Univ. of Gdansk, Gdansk ; Pankowski, Ł. ; Horodecki, M. ; Horodecki, P.

In this paper, 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 one-way Devetak-Winter (DW) protocol. Subsequently, the volume of bound entangled key-distillable states for m otimes n Hilbert space with m, n > 4 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 seven collective settings is proven to be optimal in number of settings.

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Information Theory, IEEE Transactions on  (Volume:54 ,  Issue: 6 )