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arXiv · 0812.3607

Symmetric extension in two-way quantum key distribution

Geir Ove Myhr·Joseph M. Renes·Andrew C. Doherty·Norbert Lütkenhaus
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Abstract

We introduce symmetric extensions of bipartite quantum states as a tool for analyzing protocols that distill secret key from quantum correlations. Whether the correlations are coming from a prepare-and-measure quantum key distribution scheme or from an entanglement-based scheme, the protocol has to produce effective states without a symmetric extension in order to succeed. By formulating the symmetric extension problem as a semidefinite program, we solve the problem for Bell-diagonal states. Applying this result to the six-state and BB84 schemes, we show that for the entangled states that cannot be distilled by current key distillation procedures, the failure can be understood in terms of a failure to break a symmetric extension.

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Geir Ove Myhr, Joseph M. Renes, Andrew C. Doherty, Norbert Lütkenhaus. 2009-05-03. Symmetric extension in two-way quantum key distribution. https://doi.org/10.1103/physreva.79.042329

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