Asymptotic correctability of Bell-diagonal quantum states and maximum tolerable bit error rates

Abstract

The general conditions are discussed which quantum state purification protocols have to fulfill in order to be capable of purifying Bell-diagonal qubit-pair states, provided they consist of steps that map Bell-diagonal states to Bell-diagonal states and they finally apply a suitably chosen Calderbank-Shor-Steane code to the outcome of such steps. As a main result a necessary and a sufficient condition on asymptotic correctability are presented, which relate this problem to the magnitude of a characteristic exponent governing the relation between bit and phase errors under the purification steps. These conditions allow a straightforward determination of maximum tolerable bit error rates of quantum key distribution protocols whose security analysis can be reduced to the purification of Bell-diagonal states.

21 pages

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• Symmetric extendibility for qudits and tolerable error rates in quantum cryptography
• Asymptotic correctability of Bell-diagonal qudit states and lower bounds on tolerable error probabilities in quantum cryptography
• Cyclic Mutually Unbiased Bases and Quantum Public-Key Encryption
• Postponement of dark-count effects in practical quantum key-distribution by two-way post-processing