Gaussian Quadrature Inference for Multicarrier Continuous-Variable Quantum Key Distribution

TL;DR

This paper introduces the Gaussian quadrature inference (GQI) method for multicarrier continuous-variable quantum key distribution, providing minimal error estimation of quantum state quadratures from noisy measurements and enabling practical, low-complexity implementation.

Contribution

The paper presents a novel GQI framework for multicarrier CVQKD, including the DGQI variant, with theoretical minimal error bounds and new secret key rate formulas based on statistical functions.

Findings

GQI achieves minimal quadrature estimation error.

DGQI attains the theoretical minimal magnitude error.

Secret key rate formulas are derived for multicarrier CVQKD with multiuser schemes.

Abstract

We propose the Gaussian quadrature inference (GQI) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The GQI framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. GQI utilizes the fundamentals of regularization theory and statistical information processing. We characterize GQI for multicarrier CVQKD, and define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We demonstrate the results through the adaptive multicarrier quadrature division (AMQD) scheme. We define direct GQI (DGQI), and prove that it achieves a theoretical minimal magnitude error. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of GQI. We prove the secret key rate formulas for a multiple access multicarrier CVQKD via the AMQD-MQA (multiuser quadrature allocation) scheme. The GQI and DGQI frameworks can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario.