We treat privacy in a network of quantum sensors where accessible information is limited to specific functions of the network parameters, and all other information remains private. We develop an analysis of privacy in terms of a manipulation of the quantum Fisher information matrix, and find the optimal state achieving maximum privacy in the estimation of linear combination of the unknown parameters in a network of quantum sensors. We also discuss the effect of uncorrelated noise on the privacy of the network. Moreover, we illustrate our results with an example where the goal is to estimate the average value of the unknown parameters in the network. In this example, we also introduce the notion of quasiprivacy (ε privacy), quantifying how close the state is to being private.
We treat privacy in a network of quantum sensors where accessible information is limited to specific functions of the network parameters, and all other information remains private. We develop an analysis of privacy in terms of a manipulation of the quantum Fisher information matrix, and find the optimal state achieving maximum privacy in the estimation of linear combination of the unknown parameters in a network of quantum sensors. We also discuss the effect of uncorrelated noise on the privacy of the network. Moreover, we illustrate our results with an example where the goal is to estimate the average value of the unknown parameters in the network. In this example, we also introduce the notion of quasiprivacy (ε privacy), quantifying how close the state is to being private.
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.
Anonymity and privacy are two key properties of modern communication networks. In quantum networks, distributed quantum sensing has emerged as a powerful use case, with applications to clock synchronization, detecting gravitational effects, and more. In this work, we develop a new protocol that, for the first time, combines the different cryptographic properties of anonymity and privacy for the task of distributed parameter estimation. That is, we present a protocol that allows a selected subset of network participants to anonymously collaborate in estimating the average of their private parameters. Crucially, this is achieved without disclosing either the individual parameter values or the identities of the participants, neither to each other nor to the broader network.
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.
Privacy is a fundamental requirement in distributed quantum sensor networks, where multiple clients estimate spatially distributed parameters using shared quantum resources while interacting with potentially untrusted servers. Despite its importance, existing privacy conditions rely on idealized quantum bounds and do not fully capture the operational constraints imposed by realistic measurements. Here, we introduce a universal operational privacy framework for distributed quantum sensing, formulated in terms of the experimentally accessible Fisher information matrix and applicable to arbitrary protocols characterized by singular information structures. The proposed condition provides a protocol-independent criterion, ensuring that no information about individual parameters is accessible to untrusted parties. We further experimentally demonstrate that a distributed quantum sensing protocol employing fewer photons than the number of estimated parameters simultaneously satisfies the universal privacy condition and achieves Heisenberg-limited precision. Our results establish universal operational constraints governing privacy in distributed quantum sensor networks and provide a foundation for practical, privacy-preserving quantum sensing beyond full-rank regimes.
Quantum sensor networks (QSN) typically encode N unknown parameters while targeting a single linear combination, rendering the N-1 remaining parameters as nuisance directions. To rigorously quantify estimation precision under such nuisances, we use the effective quantum Fisher information (EQFI) and establish a ``barrel-effect'' bottleneck: the global EQFI cannot exceed the weakest weighted local sensing capacity. To elucidate the information allocation mechanism underlying this bottleneck, we derive an exact local--global phase map that delineates how the trade-off between local and global EQFI depends dynamically on quantum correlations, and accordingly we identify concrete conditions for saturating the bottleneck bound. Notably, this geometric map uncovers a counterintuitive ``overcorrelated'' regime where excessive correlations actively degrade both local and global performance. Finally, we apply the phase map to intrinsic local privacy and identify the condition under which every local parameter is inaccessible while the desired global combination remains estimable. Overall, our work provides a principled methodology for engineering optimal network states in quantum sensing architectures.
Abstract Quantum networks can enhance both security and privacy conditions for multi-user communication, delegated computation, and distributed sensing tasks. In distributed quantum sensing, it is often desirable to extract only global information from a network of sensors while keeping individual sensor values hidden. Private parameter estimation (PPE), a recently proposed protocol, formalises this requirement by defining a notion of privacy that bounds information leakage about local parameters while allowing estimation of a global function. Here, we present a proof-of-principle implementation of PPE using a three-photon Greenberger–Horne–Zeilinger state distributed across three sensors and verified via stabiliser measurements. We demonstrate Heisenberg-limited scaling for the global parameter while suppressing local metrological information by up to three orders of magnitude, establishing both the privacy and precision performance of the protocol. This work, which integrates privacy in distributed quantum sensing, marks a crucial step towards developing advanced quantum-secure-and-private protocols in complex quantum networks.