Letters in Mathematical Physics

, Volume 92, Issue 1, pp 67–79 | Cite as

On the Geometric Distance Between Quantum States with Positive Partial Transposition and Private States

Article

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, irrespective of whether they are in our special class or not. Thus, our result naturally leads to the conjecture of impossibility of using PPT-bound entangled state in physical implementation of quantum key distribution.

Mathematics Subject Classification (2000)

81P68 46B20 47N50 

Keywords

bound entangled state private state trace-norm distance positive partial transposition (PPT) 

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Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.Institute for Quantum Information ScienceUniversity of CalgaryAlbertaCanada

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