Properties of multi-moded phase-randomized coherent states

Abstract

Phase-randomized coherent states are widely used in decoy-state quantum key distribution protocols with phase-coding. From the perspective of future development of quantum protocol architecture, it is important to determine whether phase randomization can be applied at an arbitrary stage of an optical scheme without affecting the informational properties of the quantum system. In this paper, using the superoperator formalism, we have shown that phase randomization of a two-mode coherent state commutes with linear optical transformations. This implies that phase randomization can be applied virtually at any point within the optical setup. We further demonstrate that the Holevo bound for such a state coincides with that of regular coherent states, bearing in mind that the Holevo bound quantifies the maximum amount of information accessible to an eavesdropper. These findings indicate that phase randomization can be directly applied to subcarrier wave quantum key distribution systems.