Trusted quantum remote sensing based on self-testing of entangled states

Abstract

In a typical scenario of quantum remote sensing, a server at the remote site sends the sensing information to the local site, so that the client there can make a diagnosis about the sensed field. In practice, the reliability of the sensing information may be undermined by kinds of errors, e.g., the imperfections of measurement devices or the attacks from a malicious eavesdropper. An alternative way to circumvent this problem is to encode the sensing information into entangled states, of which the form can be inferred in a device-independent manner, namely, self-testing. In this paper, we propose a protocol to make secure sensing of a parameter at the remote side. Upon receiving the remote sensing data, the local client can figure out the parameter range by inspecting the joint probabilities. In stark contrast, a malicious eavesdropper who is allowed to access all the remote data cannot either acquire the information of the parameter or cheat the client by replacing returned data with fake ones. We apply this protocol to a magnetic sensing scenario, and we show that the client can reliably estimate the strength range of the magnetic field, which could be intimately related to various mineral resources. Consequently, the client should not overslip any mineral resources by identifying the upper bound of magnetic strength. We also show that our protocol is valid even if the entangled states are mildly noisy.