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

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

2005-10-06

arxiv.org/abs/quant-ph/0510041v1

J. Phys. A: Math. Gen. 39 (2006), 1701-1716

Physics

Quantum Physics

21 pages

Scientific paper

10.1088/0305-4470/39/7/014

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.

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