Optimum Probe Parameters for Entangling Probe in Quantum Key Distribution

For the four-state protocol of quantum key distribution, optimum sets of probe parameters are calculated for the most general unitary probe in which each individual transmitted photon is made to interact with the probe so that the signal and the probe are left in an entangled state, and projective measurement by the probe, made subsequent to projective measurement by the legitimate receiver, yields information about the signal 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 the legitimate receiver. An arbitrary angle is included between the nonorthogonal linear polarization states of the signal photons. Two sets of optimum probe parameters are determined which both correspond to the same optimization. Also, a larger set of optimum probe parameters is found than was known previously for the standard BB84 protocol. A detailed comparison is made between the complete and incomplete optimizations, and the latter simpler optimization is also made complete. Also, the process of key distillation from the quantum transmission in quantum key distribution is reviewed, with the objective of calculating the secrecy capacity of the four-state protocol in the presence of the eavesdropping probe. Emphasis is placed on information leakage to the probe.