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arXiv · 0904.0295

On the geometric distance between quantum states with positive partial transposition and private states

Jeong San Kim·Barry C. Sanders
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Abstract

We prove an analytic positive lower bound for the geometric distance between entangled positive partial transpose (PPT) states of a broad class and any private state that delivers one secure key bit. Our proof holds for any Hilbert space of finite dimension. Although our result is proven for a specific class of PPT states, we show that our bound nonetheless holds for all known entangled PPT states with non-zero distillable key rates whether or not they are in our special class.

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Jeong San Kim, Barry C. Sanders. 2009-04-02. On the geometric distance between quantum states with positive partial transposition and private states. https://doi.org/10.1007/s11005-010-0376-6

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