Symmetric extension in two-way quantum key distribution

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.

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

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Cited by in corpus (20)

• Symmetric Extension of Two-Qubit States
• Quantum correlations of two-qubit states with one maximally mixed marginal
• Spectrum conditions for symmetric extendible states
• Designing Quantum Information Processing via Structural Physical Approximation
• Quantum Convex Support
• Extendibility of bosonic Gaussian states
• Numerical evidence for bound secrecy from two-way post-processing in quantum key distribution
• Symmetric extension of bipartite quantum states and its use in quantum key distribution with two-way postprocessing
• Symmetric extendibility for qudits and tolerable error rates in quantum cryptography
• Reducible Correlations in Dicke States
• Symmetric extendibility for a class of qudit states
• Quantifying the unextendibility of entanglement
• Symmetric extendibility of quantum states
• Measurement-Protected Quantum Key Distribution
• Hybrid Zero-capacity Channels
• Symmetric vs. bosonic extension for bipartite states
• Entanglement of temporal sections as quantum histories and their quantum correlation bounds
• Quantum Chernoff divergence in advantage distillation for quantum key distribution and device-independent quantum key distribution
• Measurement-device-independent Schmidt number certification of all entangled states
• Efficient bounds on quantum communication rates via their reduced variants