Quantum Fingerprinting over AWGN Channels with Power-Limited Optical Signals

TL;DR

This paper demonstrates that quantum fingerprinting with optical signals over noisy channels can outperform classical methods by reducing the required signal duration, especially under low-power, high-noise conditions.

Contribution

It quantifies the advantage of quantum fingerprinting over classical protocols in noisy optical channels with power constraints, revealing a distinct scaling behavior.

Findings

Quantum fingerprinting outperforms classical protocols in noisy optical channels.

Signal duration scales as O(√n) under significant noise, with quantum advantage reducing the multiplicative factor.

A noise parameter separates near-noiseless and noisy regimes, affecting protocol performance.

Abstract

Quantum fingerprinting reduces communication complexity of determination whether two $n$-bit long inputs are equal or different in the simultaneous message passing model. Here we quantify the advantage of quantum fingerprinting over classical protocols when communication is carried out using optical signals with limited power and unrestricted bandwidth propagating over additive white Gaussian noise (AWGN) channels with power spectral density (PSD) much less than one photon per unit time and unit bandwidth. We identify a noise parameter whose order of magnitude separates near-noiseless quantum fingerprinting, with signal duration effectively independent of $n$, from a regime where the impact of AWGN is significant. In the latter case the signal duration is found to scale as $O(\sqrt{n})$, analogously to classical fingerprinting. However, the dependence of the signal duration on the AWGN PSD is starkly distinct, leading to quantum advantage in the form of a reduced multiplicative factor in $O(\sqrt{n})$ scaling.