Quantum remote sensing under the effect of dephasing

TL;DR

This paper analyzes the robustness of quantum remote sensing under dephasing noise, showing how noise affects measurement uncertainty and information security, and establishing conditions for maintaining asymmetric information gain.

Contribution

It investigates the impact of dephasing and state preparation errors on quantum remote sensing performance, providing insights into its practical viability under realistic noise conditions.

Findings

Uncertainty decreases with the square root of repetitions for small M

At large M, uncertainty decreases logarithmically due to errors

Conditions are derived to maintain asymmetric information gain under noise

Abstract

The quantum remote sensing (QRS) is a scheme to add security about the measurement results of a qubit-based sensor. A client delegates a measurement task to a remote server that has a quantum sensor, and eavesdropper (Eve) steals every classical information stored in the server side. By using quantum properties, the QRS provides an asymmetricity about the information gain where the client gets more information about the sensing results than Eve. However, quantum states are fragile against decoherence, and so it is not clear whether such a QRS is practically useful under the effect of realistic noise. Here, we investigate the performance of the QRS with dephasing during the interaction with the target fields. In the QRS, the client and server need to share a Bell pair, and an imperfection of the Bell pair leads to a state preparation error in a systematic way on the server side for the sensing. We consider the effect of both dephasing and state preparation error. The uncertainty of the client side decreases with the square root of the repetition number $M$ for small $M$, which is the same scaling as the standard quantum metrology. On the other hand, for large $M$, the state preparation error becomes as relevant as the dephasing, and the uncertainty decreases logarithmically with $M$. We compare the information gain between the client and Eve. This leads us to obtain the conditions for the asymmetric gain to be maintained even under the effect of dephasing.