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.
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.
Quantum metrology aims to enhance the precision of various measurement tasks by taking advantages of quantum properties. In many scenarios, precision is not the sole target; the acquired information must be protected once it is generated in the sensing process. Considering a remote sensing scenario where a local site performs cooperative sensing with a remote site to collect sensitive information at the remote site, the loss of sensing data inevitably causes sensitive information to be revealed. Quantum key distribution is known to be a reliable solution for secure data transmission; however, it fails if an eavesdropper accesses the sensing data generated at a remote site. In this study we demonstrate that, by sharing entanglement between local and remote sites, secure quantum remote sensing can be realized, and the secure level is characterized by asymmetric Fisher information gain. Concretely, only the local site can acquire the estimated parameter accurately with Fisher information approaching 1. In contrast, the accessible Fisher information for an eavesdropper is nearly zero even if he or she obtains the raw sensing data at the remote site. This achievement is primarily due to the nonlocal calibration and control of the probe state at the remote site. Our results explore one significant advantage of ``quantumness'' and extend the notion of quantum metrology to the security realm.
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. Then, we can quantify how much information the client can gain while preserving the information asymmetricity.
Typically, the aim of quantum metrology is to sense target fields with high precision utilizing quantum properties. Unlike the typical aim, in this paper, we use quantum properties for adding a functionality to quantum sensors. More concretely, we propose a delegated quantum sensor (a client-server model) with security inbuilt. Suppose that a client wants to measure some target fields with high precision, but he/she does not have any high-precision sensor. This leads the client to delegate the sensing to a remote server who possesses a high-precision sensor. The client gives the server instructions about how to control the sensor. The server lets the sensor interact with the target fields in accordance with the instructions, and then sends the sensing measurement results to the client. In this case, since the server knows the control process and readout results of the sensor, the information of the target fields is available not only for the client but also for the server. We show that, by using an entanglement between the client and the server, an asymmetric information gain is possible so that only the client can obtain sufficient information on the target fields. In our scheme, the server generates the entanglement between a solid-state system (that can interact with the target fields) and a photon, and sends the photon to the client. On the other hand, the client is required to possess linear-optics elements only including wave plates, polarizing beam splitters, and single-photon detectors. Our scheme is feasible with the current technology, and our results pave the way for an application of quantum metrology.
The distribution of quantum sensors on quantum networks is a key enabler of quantum technologies in interferometry, gravimetry, timekeeping, biological monitoring, and beyond. Yet, guaranteeing the security of these distributed sensors over noisy, insecure networks remains a formidable challenge. Previous efforts to combine quantum metrology and cryptography have encountered an apparently unavoidable tension, proposing bounds for security which are only loosely tied to the achievable measurement performance.
Here we introduce a quantum remote sensing protocol that can rigorously certify privacy and integrity of the estimation. By employing offline bilateral Pauli-twirling, our approach forces the effective quantum channel into a Bell-diagonal form, independently of the attack. Surprisingly, this also preserves metrological sensitivity without introducing additional experimental overhead. Relying solely on public communication alongside an insecure quantum link, the protocol enables legitimate users to exactly quantify their estimation error relative to an eavesdropper controlling the channels.
We experimentally demonstrate this framework by estimating an optical phase using entangled photons, observing that the users' precision consistently surpasses the eavesdropper's capabilities across a broad parameter regime. By unifying quantum cryptography and metrology, our results provide a practical pathway to achieve simultaneous quantum-limited precision and rigorous information security in real-world quantum networks.
Quantum entanglement is the key resource for quantum information processing. Device-independent certification of entangled states is a long standing open question, which arouses the concept of self-testing. The central aim of self-testing is to certify the state and measurements of quantum systems without any knowledge of their inner workings, even when the used devices cannot be trusted. Specifically, utilizing Bell's theorem, it is possible to place a boundary on the singlet fidelity of entangled qubits. Here, beyond this rough estimation, we experimentally demonstrate a complete self-testing process for various pure bipartite entangled states up to four dimensions, by simply inspecting the correlations of the measurement outcomes. We show that this self-testing process can certify the exact form of entangled states with fidelities higher than 99.9% for all the investigated scenarios, which indicates the superior completeness and robustness of this method. Our work promotes self-testing as a practical tool for developing quantum techniques.
Private remote quantum sensing 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 analyze a private remote sensing protocol 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.