Private Remote Phase Estimation over a Lossy Quantum Channel

TL;DR

The 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.

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.

Figures (2)

• Figure 1: Schematic depiction of our PRQS protocol. Alice wants to estimate a phase $\phi$ at Bob's location, out of her reach. She thus delegates the measurement to Bob, who performs heterodyne on the transmitted probes. Eve compromises the security of the protocol by tapping part of the signal, in order to learn the initial phase, and can also access any classical communication between the parties.
• Figure 2: Plots of the finite-size and first-order asymptotic ($N=100$) behaviour of the estimation error ${\rm MSE}_{A}$ (a,b) and privacy ${\mathcal{P}}$ (c,d), as a function of the initial probes' mean-photon number $\alpha^2$ (a,c) and channel transmissivity $\eta$.