Two-party secure quantum remote sensing protocols enable quantum-enhanced measurements at remote locations with guaranteed security against eavesdroppers. This idea can be scaled up to networks of nodes where one party can directly measure functions of parameters at the different nodes using entangled states. However, the security on such networks decreases exponentially with the number of nodes. Here we show how this problem can be overcome in a hybrid protocol that utilizes both entangled and separable states to achieve quantum-enhanced measurement precision and security on networks of any size.
Two-party secure quantum remote sensing protocols enable quantum-enhanced measurements at remote locations with guaranteed security against eavesdroppers. This idea can be scaled up to networks of nodes where one party can directly measure functions of parameters at the different nodes using entangled states. However, the security on such networks decreases exponentially with the number of nodes. Here we show how this problem can be overcome in a hybrid protocol that utilizes both entangled and separable states to achieve quantum-enhanced measurement precision and security on networks of any size.
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 sensing is a promising technology capable of demonstrating clear advantage over comparable classical techniques for precise measurement. One application of quantum sensing is in function estimation, which can be done using a network of entangled quantum sensors, allowing for measurements with greater optimal sensitivity than unentangled sensing protocols. In cases where quantum sensor networks will be used to measure data that should remain private (e.g., biomedical data), it is imperative that these protocols include a privacy mechanism to hide sensitive information. In this work, we show that entangled sensor networks are vulnerable to certain privacy-violating attacks. To mitigate these attacks, we introduce secure sensing protocols endowed with differential privacy. We reconcile differential privacy with retaining Heisenberg-limited scaling, and introduce several protocols achieving varying balances between the two. We show that our main protocol, an n-node network sensing protocol that injects noise directly into the sensing Hamiltonian, exhibits a tradeoff between the desirable O(1/n2) Heisenberg scaling of the mean-squared error of the function estimate and the level of privacy attainable. Under assumptions on the network (a common source of randomness and a constant fraction of honest parties), we show that this protocol is locally implementable and achieves (O(1),δ)-differential privacy for arbitrarily small δ while retaining Heisenberg scaling of the mean-squared error. We prove that our protocols are resilient to attacks by broad classes of classical and quantum adversaries, and find advantages in the privacy-utility tradeoff when using quantum techniques.
Entangling distant quantum sensors is a key application of future quantum networks, allowing for the estimation of global functions of local parameters, with precision that is not possible with stand-alone, individual, quantum sensors. However, with this advantage comes the risk of information leakage over the network via possible malicious parties. It is often particularly important that local parameters remain unknown and that only the global function is shared across the network. Recently, the notion of privacy has been introduced in this context, which ensures that only the agreed function of parameters is shared over the network, even when malicious parties control the network itself, whilst maintaining the estimation advantage. In this work, we introduce a noise-robust protocol for private quantum networked sensing, which we realise using a high-fidelity Greenberger-Horne-Zeilinger (GHZ) state source. We further run a comparative analysis and simulate attacks using three different quantum states, a four-qubit GHZ state, two Bell pairs, and a fully separable state. Our results highlight the clear advantage of GHZ states in maintaining high precision, accuracy, and privacy for the distributed estimation task.
Quantum secure metrology protocols harness quantum effects to probe remote systems with enhanced precision and security. Traditional QSM protocols require multi-partite entanglement, which limits its near-term implementation due to technological constraints. This paper proposes a QSM scheme that employs Bell pairs to provide unconditional security while offering precision scaling beyond the standard quantum limit. We provide a detailed comparative performance analysis of our proposal under multiple attacks. We found that the employed controlled encoding strategy is far better than the parallel encoding of multi-partite entangled states with regard to the secrecy of the parameter. We also identify and characterize an intrinsic trade-off relationship between the maximum achievable precision and security under the limited availability of resources. The dynamic scalability of the proposed protocol makes it suitable for large-scale network sensing scenarios.
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.
Any two-party cryptographic primitive can be implemented using quantum communication under the assumption that it is difficult to store a large number of quantum states perfectly. However, achieving reliable quantum communication over long distances remains a difficult problem. Here, we consider a large network of nodes with only neighboring quantum links. We exploit properties of this cloud of nodes to enable any two nodes to achieve security even if they are not directly connected. Our results are based on techniques from classical cryptography and do not resort to technologically difficult procedures like entanglement swapping. More precisely, we show that oblivious transfer can be achieved in such a network if and only if there exists a path in the network between the sender and the receiver along which all nodes are honest. Finally, we show that useful notions of security can still be achieved when we relax the assumption of an honest path. For example, we show that we can combine our protocol for oblivious transfer with computational assumptions such that we obtain security if either there exists an honest path, or, as a backup, at least the adversary cannot solve a computational problem.