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Symmetric extension in two-way quantum key distribution

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Luetkenhaus,  Norbert
Max Planck Research Group, Max Planck Institute for the Science of Light, Max Planck Society;

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Citation

Myhr, G. O., Renes, J. M., Doherty, A. C., & Luetkenhaus, N. (2009). Symmetric extension in two-way quantum key distribution. PHYSICAL REVIEW A, 79(4): 042329. doi:10.1103/PhysRevA.79.042329.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002D-6C01-3
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 Bennett-Brassard 1984 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.