Performance of quantum data transmission systems in the presence of thermal noise

TL;DR

This paper evaluates quantum data transmission performance under thermal noise using an approximation approach, demonstrating quantum detection's superiority over classical methods despite non-optimality.

Contribution

It introduces an approximation method for analyzing noisy quantum states and compares its accuracy with exact solutions, applying it to modulation schemes.

Findings

SRM approach provides accurate performance estimates.

Quantum detection outperforms classical homodyne detection.

Approximate methods are effective for complex quantum noise analysis.

Abstract

In the literature the performance of quantum data transmission systems is usually evaluated in the absence of thermal noise. A more realistic approach taking into account the thermal noise is intrinsically more difficult because it requires dealing with Glauber coherent states in an infinite--dimensional space. In particular, the exact evaluation of the optimal measurement operators is a very difficult task, and numerical approximation is unavoidable. The paper faces the problem by approximating the P-representation of the noisy quantum states with a large but finite number of terms and applying to them the square root measurement (SRM) approach. Comparisons with the exact solution obtained with convex semidefinite programming show that the SRM approach gives quite accurate results. As application, the performance of quadrature amplitude modulation (QAM) and phase shift keying (PSK) systems is considered. In spite of the fact that the SRM approach is not optimal and overestimates the error probability, also in these cases the quantum detection maintains its superiority with respect to the classical homodyne detection.