Optimized unitary transformation for BB84 entangling probe

Howard E. Brandt

doi:10.1117/12.540875

24 August 2004 Optimized unitary transformation for BB84 entangling probe

Howard E. Brandt

Proceedings Volume 5436, Quantum Information and Computation II; (2004) https://doi.org/10.1117/12.540875
Event: Defense and Security, 2004, Orlando, Florida, United States

Abstract

The standard four-state (BB84) protocol of key distribution in quantum cryptography, Slutsky, Rao, Sun, and Fainman performed an eavesdropping probe optimization, which an average yields the most information to the eavesdropper for a given error rate caused by the probe. The most general possible probe consistent with unitary was considered, in which each individual transmitted bit is made to interact with the probe so that the carrier and the probe are left in an endangered state, and measurement by the probe, made subsequent to measurement by the legitimate receiver, yield information about the carrier state. The probe optimization is based on maximizing the Renyi information gain by the probe on corrected data for a given error rate induced by the probe in a legitimate receiver. The results were obtained for the standard protocol with an angle of 45 degrees between the signal bases. In more recent work, a larger set of optimum probe parameters was found than was known previously, and although they all yield the same maximum Renyi information gain by the probe, alternative options are made available for optimum probe design. In the present work, the corresponding optimized unitary transformation, representing the action of the probe on the signal, are calculated. I have determined three classes of unitary transformations yielding the same maximum information to the probe. The simplest one corresponds to a probe having a two-dimensional Hilbert space of states, and is uniquely determined by the error rate. The second class corresponds to a probe having a four-dimensional Hilbert space of states, and is determined by the error rate and two continuous angle parameters, which are mutually constrained by the error rate. The third class corresponds to a probe having a four-dimensional Hilbert space, and is determined by the error rate and two continuous angle parameters, one of which is constrained by the error rate. This work will be useful in the design of an optimum-entangling probe.

Citation Download Citation

Howard E. Brandt "Optimized unitary transformation for BB84 entangling probe", Proc. SPIE 5436, Quantum Information and Computation II, (24 August 2004); https://doi.org/10.1117/12.540875

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