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Optical Fiber Communication Conference

Monitoring the inconclusive rate in quantum key distribution

Howard E. Brandt

Published Jan 1, 2001• 0 citations
Publisher

Abstract

Based on recent analyses of the inconclusive rate as a disturbance measure in quantum cryptography [Phys. Rev. A 62, 042310 (2000)], the least-effective inconclusive-rate monitoring threshold is calculated for a POVM quantum key receiver disturbed by a general unitary probe.
DOI
10.1364/icqi.2001.pa2

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The inclusive rate is considered as a disturbance measure in key distribution in quantum cryptography. Bennett's two- state protocol is addressed for the case in which a positive operator valued measure is implemented by the legitimate receiver in the presence of individual attack by a general unitary disturbing eavesdropping probe. The maximum Renyi information gain by the disturbing probe is calculated for given receiver error and inconclusive rates. It is demonstrated explicitly that less information is available to an eavesdropper at fixed inconclusive rate and error rate than is available at fixed error rate only.
After summarizing a recent calculation of the maximum Renyi information loss (for fixed error and inconclusive rates) from a positive operator valued measure (POVM) quantum cryptographic receiver to a general unitary probe, I calculate the worst inconclusive rate for the legitimate receiver. Disturbed inconclusive rates are considered which are less, as well as greater, than the unperturbed inconclusive rate. I also demonstrate that for an optimized individual attack there is a minimum induced error rate which is fixed by the induced inconclusive rate.
The inconclusive rate is considered as a disturbance measure in key distribution in quantum cryptography. Bennett's two-state protocol is addressed for the case in which a positive operator-valued measure is implemented by the legitimate receiver in the presence of an individual attack by a general unitary disturbing eavesdropping probe. The maximum Renyi information gain by the disturbing probe is calculated for given receiver error and inconclusive rates. It is demonstrated explicitly that less information is available to an eavesdropper at a fixed inconclusive rate and error rate than is available at a fixed error rate only.
Summary form only given. The inconclusive rate can be a useful disturbance measure in quantum cryptography. Bennett's two-state protocol is considered for the case in which a positive operator-valued measure is optically implemented by the legitimate receiver in the presence of an individual attack by a general unitary disturbing eavesdropping probe. The maximum Renyi information gain by the disturbing probe is calculated for given receiver error and inconclusive rates. It is shown explicitly that less information is available to an eavesdropper at fixed inconclusive rate and error rate than is available at fixed error rate only.
It is demonstrated that the eavesdropping optimization obtained recently by Slutsky et al. [Phys. Rev. A 57, 2383 (1998)] for Bennett's two-state protocol of key distribution in quantum cryptography holds, not only for the case in which an ordinary von Neumann projective measure is implemented by the legitimate receiver, but also for the case in which a positive operator-valued measure is implemented, as in Brandt et al. [Phys. Rev. A 56, 4456 (1997)]. In both cases, identical expressions hold for both the Renyi information gained by the eavesdropper and for the error rate induced by the eavesdropper in terms of the parameters characterizing the key distribution system and the eavesdropper's probe.