Abstract
We develop a general theory for quantum key distribution (QKD) in both the forward error correction and the reverse error correction cases when the QKD system is equipped with phase-randomized coherent light with an arbitrary number of decoy intensities. For this purpose, generalizing Wang's expansion, we derive a convex expansion of the phase-randomized coherent state. We also numerically check that the asymptotic key generation rates are almost saturated when the number of decoy intensities is three.
Highlights
The BB84 protocol proposed by Bennett and Brassard[1] has been known as a famous protocol guaranteeing information theoretical security
By generalizing Wang’s expansion, we have derived a convex expansion of the phaserandomized coherent state, which allows us to parameterize Eve’s operation using 3k +3 parameters even in the general case
Lower bound of asymptotic key generation (AKG) rate has been obtained with k decoy intensities
Summary
The BB84 protocol proposed by Bennett and Brassard[1] has been known as a famous protocol guaranteeing information theoretical security. We obtain three constraint equations with four unknown parameters He derived an estimate of the counting rate of the single photon state. We treat the case of arbitrary number k of decoy intensities with BBL formulas when the intensity can be controlled§ For this purpose, we generalize Wang’s expansion of the phase-randomized coherent states, in which k + 1 phase-randomized coherent states are given by convex combinations of k + 2 states, which are called basis states. It is needed to give the AKG rate formula by using the counting rates and the phase error rates of each intensities based on this expansion For this purpose, we generalize mean value theorem and the concept of “difference”.
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