Symmetric extension in two-way quantum key distribution

Details Symmetric extension in two-way quantum key distribution Symmetric extension in two-way quantum key distribution

2008-12-18

arxiv.org/abs/0812.3607v2

Phys. Rev. A 79, 042329 (2009)

Physics

Quantum Physics

11 pages, 2 figures; v2: published version, hyperlinked references

Scientific paper

10.1103/PhysRevA.79.042329

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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