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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

POVM inconclusive rate

Howard E. Brandt

Published Jul 13, 2000• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.391956

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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.
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.
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.
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.
A design is given for an optimized entangling probe attacking the BB84 (Bennett-Brassard 1984) protocol of quantum key distribution and yielding maximum information to the probe for a full range of induced error rates. Probe photon polarization states become optimally entangled with the signal states on their way between the legitimate transmitter and receiver. Although standard von-Neumann projective measurements of the probe yield maximum information on the pre-privacy amplified key, if instead the probe measurements are performed with a certain positive operator valued measure, then the measurement results are conclusive, at least some of the time, for a full range of inconclusive rates.