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arXiv:2007.15903 · Physical Review A

Quantum remote sensing under the effect of dephasing

Hideaki Okane, Hideaki Hakoshima, Yuki Takeuchi, Yuya Seki, Yuichiro Matsuzaki

Published Dec 10, 2021• 22 citations
arXivHTMLPDF

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. Then, we can quantify how much information the client can gain while preserving the information asymmetricity.

DOI
10.1103/physreva.104.062610

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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 MMM for small MMM, which is the same scaling as the standard quantum metrology. On the other hand, for large MMM, the state preparation error becomes as relevant as the dephasing, and the uncertainty decreases logarithmically with MMM. 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.
Quantum sensors have the potential to outperform their classical counterparts. For classical sensing, the uncertainty of the estimation of the target fields scales inversely with the square root of the measurement time T. On the other hand, by using quantum resources, we can reduce this scaling of the uncertainty with time to 1/T. However, as quantum states are susceptible to dephasing, it has not been clear whether we can achieve sensitivities with a scaling of 1/T for a measurement time longer than the coherence time. Here, we propose a scheme that estimates the amplitude of globally applied fields with the uncertainty of 1/T for an arbitrary time scale under the effect of dephasing. We use one-way quantum-computing-based teleportation between qubits to prevent any increase in the correlation between the quantum state and its local environment from building up and have shown that such a teleportation protocol can suppress the local dephasing while the information from the target fields keeps growing. Our method has the potential to realize a quantum sensor with a sensitivity far beyond that of any classical sensor.
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 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.
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 sensors have the potential to outperform their classical counterparts. For classical sensing, the uncertainty of the estimation of the target fields decreases 1/T1/\sqrt{T}1/T​ with measurement time TTT. On the other hand, by using quantum resources, one can decrease the uncertainty with time to 1/T1/T1/T - the Heisenberg limit. However as quantum states are susceptible to dephasing, it has been not clear whether one can achieve the Heisenberg limit for a measurement time scaling longer than the coherence time of those states. Here, we propose a scheme that estimates the amplitude of globally applied fields with Heisenberg limited sensitivity in principle for an arbitrary time scale under the effect of dephasing. We use one way quantum computing based teleportation between qubits to prevent the correlation between the quantum state and its local environment from increasing, and have shown that such a teleportation protocol can suppress the local dephasing while the information from the target fields keeps growing. Our methods has the potential to realize a quantum sensor with a sensitivity far beyond that of any classical sensors.