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arXiv:2307.07758 · Physical Review Letters

Quantum-Enhanced Metrology with Network States

Yuxiang Yang, Benjamin Yadin, Zhen‐Peng Xu

Published May 20, 2024• 24 citations
arXivHTMLPDF

Abstract

Armed with quantum correlations, quantum sensors in a network have shown the potential to outclass their classical counterparts in distributed sensing tasks such as clock synchronization and reference frame alignment. On the other hand, this analysis was done for simple and idealized networks, whereas the correlation shared within a practical quantum network, captured by the notion of network states, is much more complex. Here, we prove a general bound that limits the performance of using quantum network states to estimate a global parameter, establishing the necessity of genuine multipartite entanglement for achieving a quantum advantage. The bound can also serve as an entanglement witness in networks and can be generalized to states generated by shallow circuits. Moreover, while our bound prohibits local network states from achieving the Heisenberg limit, we design a probabilistic protocol that, once successful, attains this ultimate limit of quantum metrology and preserves the privacy of involved parties. Our work establishes both the limitation and the possibility of quantum metrology within quantum networks.

DOI
10.1103/physrevlett.132.210801

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Armed with quantum correlations, quantum sensors in a network have shown the potential to outclass their classical counterparts in distributed sensing tasks such as clock synchronization and reference frame alignment. On the other hand, this analysis was done for simple and idealized networks, whereas the correlation shared within a practical quantum network, captured by the notion of network states, is much more complex. Here, we prove a general bound that limits the performance of using quantum network states to estimate a global parameter, establishing the necessity of genuine multipartite entanglement for achieving a quantum advantage. The bound can also serve as an entanglement witness in networks and can be generalized to states generated by shallow circuits. Moreover, while our bound prohibits local network states from achieving the Heisenberg limit, we design a probabilistic protocol that, once successful, attains this ultimate limit of quantum metrology and preserves the privacy of involved parties. Our work establishes both the limitation and the possibility of quantum metrology within quantum networks.
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.
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One of the most promising applications of quantum networks is entanglement-assisted sensing. The field of quantum metrology exploits quantum correlations to improve the precision bound for applications such as precision timekeeping, field sensing, and biological imaging. When measuring multiple spatially distributed parameters, current literature focuses on quantum entanglement in the discrete-variable case and quantum squeezing in the continuous-variable case, distributed amongst all of the sensors in a given network. However, it can be difficult to ensure that all sensors preshare entanglement of sufficiently high fidelity. This work probes the space between fully entangled and fully classical sensing networks by modeling a star network with probabilistic entanglement generation that is attempting to estimate the average of local parameters. The quantum Fisher information is used to determine which protocols best utilize entanglement as a resource for different network conditions. It is shown that without entanglement distillation there is a threshold fidelity below which classical sensing is preferable. For a network with a given number of sensors and links characterized by a certain initial fidelity and probability of success, this work outlines when and how to use entanglement, when to store it, and when it needs to be distilled.
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger-Horne-Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.
Distributed quantum sensing, which estimates a global parameter across distant nodes, has attracted significant interest for applications such as quantum imaging, sensor networks, and global-scale clock synchronization. N00N states are regarded as one of the optimal quantum resources for quantum metrology, enabling the Heisenberg scaling. Recently, the concept of N00N states has been extended to multimode N00N states for quantum-enhanced multiple-parameter estimation. However, the application of multimode N00N states in distributed quantum sensing remains unexplored. Here, we propose a distributed quantum sensing scheme that achieves the Heisenberg scaling using multimode N00N states. We theoretically show that multimode N00N states can reach the Heisenberg scaling by examining both the Cramér-Rao bound and the quantum Cramér-Rao bound. For experimental demonstration, we employ a four-mode 2002 state to estimate the average of two spatially distributed phases, achieving a 2.74 dB sensitivity enhancement over the standard quantum limit. We believe that utilizing multimode N00N states for distributed quantum sensing offers a promising approach for developing entanglement-enhanced sensor networks.
We address the metrological problem of estimating collective stochastic properties imprinted on a network of quantum sensors. Canonical examples include center-of-mass quadrature fluctuations in a system of bosonic modes and correlated dephasing in an ensemble of qubits (e.g., spins), bosons, or fermions. We develop a theoretical framework to determine the limits of correlated (weak) noise estimation with quantum sensor networks and reveal the requirements for entanglement advantage. Notably, an advantage emerges from the synergistic interplay between quantum correlations of the sensors and "classical" correlations of the noises. We determine optimal entangled probe states and identify a sensing protocol-reminiscent of a many-body echo-that achieves the fundamental limits of measurement sensitivity for a broad class of problems, unveiling a route toward entanglement-enhanced metrology of correlated many-body phenomena.