Symmetric extension of bipartite quantum states and its use in quantum key distribution with two-way postprocessing

摘要: We investigate which bipartite quantum states admit a symmetric extension and apply the results in analysis of noise thresholds key distribution protocols with two-way postprocessing. We find that can be decomposed into convex combination a_pure_ extension. For state to have pure extension, its nonzero eigenvalues must equal one subsystems. While this does not fully characterize set all dimensions, it is full characterization for two qubits. A conjectured formula characterizing two-qubit (mixed or pure) presented. Proofs are given some special classes. multi-qubit Bell-diagonal states, simplified using symmetries formulated as semidefinite program. Quantum advantage distillation steps then analyzed. commonly used repetition code distillation, failure distill secret beyond currently known explained by break More general linear schemes analyzed, but those we they tolerate strictly less than before fail The suggest no other scheme reach threshold 27.6 % six-state protocol achieved distillation.