Private Remote Phase Estimation over a Lossy Quantum Channel

TL;DR

This paper introduces a new private remote quantum sensing protocol using continuous-variable states over lossy channels, providing tighter bounds on estimation error and privacy under realistic assumptions.

Contribution

It is the first to analyze a PRQS protocol with continuous-variable states in a lossy channel setting, improving estimation and privacy bounds with practical channel assumptions.

Findings

Tighter estimation error bounds under realistic channel models.

Quantification of privacy in finite-size and asymptotic regimes.

Validation of channel assumptions with measurement data enhances practical relevance.

Abstract

Private remote quantum sensing (PRQS) aims at estimating a parameter at a distant location by transmitting quantum states on an insecure quantum channel, limiting information leakage and disruption of the estimation itself from an adversary. Previous results highlighted that one can bound the estimation performance in terms of the observed noise. However, if no assumptions are placed on the channel model, such bounds are very loose and severely limit the estimation. We propose and analyse a PRQS using, for the first time to our knowledge, continuous-variable states in the single-user setting. Assuming a typical class of lossy attacks and employing tools from quantum communication, we calculate the true estimation error and privacy of our protocol, both in the asymptotic limit of many channel uses and in the finite-size regime. Our results show that a realistic channel-model assumption, which can be validated with measurement data, allows for a much tighter quantification of the estimation error and privacy for all practical purposes.