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

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

2009-04-02

arxiv.org/abs/0904.0295v1

Letters in Mathematical Physics 92(1): pp. 67 - 79 (2010)

Physics

Quantum Physics

16 pages

Scientific paper

10.1007/s11005-010-0376-6

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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