The rationality about the assumption that the signal and decoy states are indistinguishable in decoy-state quantum key distribution

TL;DR

This paper investigates whether the assumption that signal and decoy states are indistinguishable in decoy-state QKD is valid, using Bayesian decision and simulations, and proposes methods to optimize state intensities for security and efficiency.

Contribution

The study provides a rigorous analysis of the indistinguishability assumption in decoy-state QKD and offers practical guidelines for setting state intensities to enhance security and efficiency.

Findings

Eve's ability to distinguish states is limited under Bayesian analysis.

Decoy-state attack effectiveness is often negligible or fails.

Proper intensity setting reduces attack risk and improves efficiency.

Abstract

Decoy-state quantum key distribution (QKD) has become the most efficient method to resist the photon-number-splitting (PNS) attack and estimate the secure key rate. The decoy-state method has many assumptions, among which a critical one is that an eavesdropper (Eve) cannot distinguish between the signal and decoy states. However, a rigorous proof of the rationality about this assumption is not yet available so far. In fact, due to the difference of photon-number probability distribution between the signal and decoy states, Eve is able to distinguish the two states with a certain probability. In this work, we adopt the Bayesian decision to distinguish the signal and decoy states in one-decoy-state QKD, and perform different PNS attack strategies for the two states according to the previous decision. The numerical simulations indicate that the attack effect is not obvious or even failed. Thus, it is reasonable to assume that the signal and decoy states are indistinguishable in decoy-state QKD. In addition, we also provide the method to set the intensities of signal and decoy states properly, which can not only reduce the preparation cost and improve the communication efficiency, but also avoid the attack from Eve using the intensity difference between the signal and decoy states.