Fundamental Limits on QBER and Distance in Quantum Key Distribution

TL;DR

This paper establishes fundamental limits on the maximum tolerable QBER and transmission distance in quantum key distribution, linking theoretical capacity bounds to practical noise models for secure quantum communication.

Contribution

It derives universal bounds on QKD distance and noise tolerance based on capacity thresholds for qubit channels, applicable to various protocols and physical setups.

Findings

Maximum QBER compatible with secure QKD is established.

Upper bounds on communication distance are derived for fiber and free-space links.

Universal limits incorporate diffraction and noise constraints relevant to deep-space communication.

Abstract

Quantum key distribution (QKD) enables information-theoretic secure communication, yet its ultimate tolerance to noise and achievable transmission distance remain fundamentally constrained. We establish the maximum quantum bit error rate (QBER) compatible with secure QKD and derive corresponding upper bounds on communication distance. Our results follow from a fundamental capacity threshold for qubit Pauli channels and apply to protocols based on two or more mutually unbiased bases, using either single-photon or weak coherent sources. By connecting information-theoretic limits to realistic physical noise models, we obtain universal bounds on achievable distances in fiber and free-space links, including diffraction-limited constraints relevant to deep-space quantum communications. These findings clarify the ultimate noise robustness of QKD and delineate the fundamental boundaries of secure quantum communication.