Quantum-Key Distribution using Decoy Pulses to Combat Photon-Number Splitting by Eavesdropper: An Event-by-Event Impairment Enumeration Approach for Performance Evaluation and Design

TL;DR

The paper addresses photon-number-splitting risks in QKD under realistic optical impairments and introduces an event-by-event impairment enumeration framework for the BB84-DP-PNS protocol with decoy pulses. It derives analytical estimates of the key generation rate $R_k$, Bob's signal/decoy yields $y^{bs}$ and $y^{bd}$, and Eve's signal-to-decoy ratios $\rho^e_{sd}$ and $\rho^y_{sd}$ to guide secure operation. By integrating Poisson photon statistics, fiber losses, polarization effects, and receiver processing, it provides design guidelines for choosing signal and decoy intensities $(\lambda_s,\lambda_d)$ and pulse counts $(m_s,m_d,m_v)$ to detect eavesdropping and maintain key throughput. The framework yields practical, physics-grounded insights and can be extended to other QKD schemes.

Abstract

Quantum-key distribution (QKD) schemes employing quantum communication links are typically based on the transmission of weak optical pulses over optical fibers to setup a secret key between the transmitting and receiving nodes. Alice transmits optically a random bit stream to the receiver (Bob) through the photon polarizations or the quadrature components of the lightwaves associated with the photons, with a secret key remaining implicitly embedded therein. However, during the above transmission, some eavesdropper (Eve) might attempt to tap the passing-by photons from the optical fiber links to extract the key. In one of the popular QKD schemes, along with signal pulses, some additional decoy pulses are transmitted by Alice, while Eve might use photon-number splitting (PNS) for eavesdropping. In a typical PNS scheme, (i) the optical pulses with single photon are blocked by Eve, (ii) from the optical pulses with two photons, one photon is retained by Eve to carry out eavesdropping operation and the other is retransmitted to Bob, and (iii) all other pulses with more than two photons are retransmitted by Eve to Bob without retaining any photon from them. Extensive theoretical research has been carried out on such QKD schemes, by employing information-theoretic approach along with computer simulations and experimental studies. We present a novel event-by-event impairment enumeration approach to evaluate the overall performance of one such QKD scheme analytically with due consideration to the physical layer of the quantum communication links. The proposed approach monitors the impairments of the propagating optical pulses event-by-event at all possible locations along the optical fiber link using statistical approach, and provides estimates of the realizable key generation rate, while assuring an adequate yield ratio between signal and decoy pulses for the detection of possible eavesdropping.

Figures (3)

• Figure 1: Block schematic of QKD system using QKD-PD-PNS protocol.
• Figure 2: Plot of $R_k$ vs. $l$ with $\lambda_s = 0.5$ and $\lambda_d = 0.2$ for 50 km fiber link. Other parameters remain the same as used in Tables 3 and 4.
• Figure 3: Plots of $\rho^e_{sd}$ and $\rho^y_{sd}$ vs. $l$ with $\lambda_s = 0.5$ and $\lambda_d = 0.2$ for 50 km fiber link. Other parameters remain the same as used in Tables 3 and 4.