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arXiv:2407.18055 · Communications Physics

Collective quantum enhancement in critical quantum sensing

Uesli Alushi, Alessandro Coppo, Valentina Brosco, Roberto Di Candia, Simone Felicetti

Published Feb 22, 2025• 23 citations
arXivHTMLPDF

Abstract

Abstract Critical systems represent a valuable resource in quantum sensing and metrology. Critical quantum sensing (CQS) protocols can be realized using finite-component phase transitions, where criticality arises from the rescaling of system parameters rather than the thermodynamic limit. Here, we show that a collective quantum advantage can be achieved in a multipartite CQS protocol using a chain of parametrically coupled critical resonators in the weak-nonlinearity limit. We derive analytical solutions for the low-energy spectrum of this unconventional quantum many-body system, which is composed of locally critical elements. We then assess the scaling of the quantum Fisher information with respect to fundamental resources. We demonstrate that the coupled chain outperforms an equivalent ensemble of independent critical sensors, achieving quadratic scaling in the number of resonators. Finally, we show that even with finite Kerr nonlinearity or Markovian dissipation, the critical chain retains its advantage, making it relevant for implementing quantum sensors with current microwave superconducting technologies.

DOI
10.1038/s42005-025-01975-9

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Abstract Critical systems represent a valuable resource in quantum sensing and metrology. Critical quantum sensing (CQS) protocols can be realized using finite-component phase transitions, where criticality arises from the rescaling of system parameters rather than the thermodynamic limit. Here, we show that a collective quantum advantage can be achieved in a multipartite CQS protocol using a chain of parametrically coupled critical resonators in the weak-nonlinearity limit. We derive analytical solutions for the low-energy spectrum of this unconventional quantum many-body system, which is composed of locally critical elements. We then assess the scaling of the quantum Fisher information with respect to fundamental resources. We demonstrate that the coupled chain outperforms an equivalent ensemble of independent critical sensors, achieving quadratic scaling in the number of resonators. Finally, we show that even with finite Kerr nonlinearity or Markovian dissipation, the critical chain retains its advantage, making it relevant for implementing quantum sensors with current microwave superconducting technologies.
Quantum metrology, a cornerstone of quantum technologies, exploits entanglement and superposition to achieve higher precision than classical protocols in parameter-estimation tasks. When combined with critical phenomena such as phase transitions, the divergence of quantum fluctuations is predicted to enhance the performance of quantum sensors. Here, we implement a critical quantum sensor using a superconducting parametric (i.e., two-photon driven) Kerr resonator. The sensor, a linear resonator terminated by a superconducting quantum interference device, operates near the critical point of a finite-component second-order dissipative phase transition obtained by scaling the system parameters. We analyze the performance of a frequency-estimation protocol and show that quadratic precision scaling with respect to the system size can be achieved with finite values of the Kerr nonlinearity. Since each photon emitted from the cavity carries more information about the parameter to be estimated compared to its classical counterpart, our protocol opens up perspectives for faster or more precise metrological protocols. Our results demonstrate that quantum advantage in a sensing protocol can be achieved by exploiting a phase transition.
Abstract Critical quantum systems are a promising resource for quantum metrology applications, due to the diverging susceptibility developed in proximity of phase transitions. Here, we assess the metrological power of parametric Kerr resonators undergoing driven-dissipative phase transitions. We fully characterize the quantum Fisher information for frequency estimation, and the Helstrom bound for frequency discrimination. By going beyond the asymptotic regime, we show that the Heisenberg precision can be achieved with experimentally reachable parameters. We design protocols that exploit the critical behavior of nonlinear resonators to enhance the precision of quantum magnetometers and the fidelity of superconducting qubit readout.
Quantum phenomena offer the possibility of measuring physical quantities with precision beyond classical limits. However, current progress is constrained by scalability, environmental noise, and challenges in practical integration. This highlights the necessity for novel approaches. An emerging paradigm in this direction is , which harnesses the enhanced susceptibility and nonclassical correlations that naturally occur near quantum phase transitions as resources for quantum-enhanced precision. This tutorial provides a pedagogical introduction to key concepts and a detailed overview of prominent quantum sensing strategies that exploit critical phenomena in metrology. Through examples of increasing complexity, the reader is guided through various critical quantum sensing protocols applied to different critical systems. Special emphasis is placed on the optimal scaling of estimation precision with respect to fundamental resources. Finally, we discuss how critical quantum metrology extends from idealized models to realistic open-system, dissipative regimes, and strongly correlated fermionic systems, outlining both the challenges and opportunities for future quantum technologies.
We compare critical quantum sensing to passive quantum strategies to perform frequency estimation, in the case of single-mode quadratic Hamiltonians. We show that, while in the unitary case both strategies achieve precision scaling quadratic with the number of photons, in the presence of dissipation this is true only for critical strategies. We also establish that working at the exceptional point or beyond threshold provides suboptimal performance. This critical enhancement is due to the emergence of a transient regime in the open critical dynamics, and is invariant to temperature changes. When considering both time and system size as resources, for both strategies the precision scales linearly with the product of the total time and the number of photons, in accordance with fundamental bounds. However, we show that critical protocols outperform optimal passive strategies if preparation and measurement times are not negligible. Our results are applicable to a broad variety of critical sensors whose phenomenology can be reduced to that of a single-mode quadratic Hamiltonian, including systems described by finite-component and fully connected models.
Critical properties of a quantum system are recognized as valuable resources for quantum metrology. In this work, we investigate the criticality-enhanced sensing in a quantum Rabi triangle system, which exhibits multiple phases. Around the phase boundary, enhanced parameter estimation precision can be achieved by tuning either the scaled coupling strength or the hopping phase controlled by an artificial magnetic field. We observe that the quantum Fisher information shows divergent scaling near different quantum phase transition points, characterized by distinct critical exponents. When the resource consumption is taken into account, we find that the divergent quantum Fisher information can reach the Heisenberg limit. Furthermore, we propose a measurement scheme of the average photon number and the quantum Cramér-Rao bound can be saturated.
Quantum criticality has been demonstrated as a useful quantum resource for parameter estimation. This includes second-order, topological and localization transitions. In all these works reported so far, gap-to-gapless transition at criticality has been identified as a crucial resource for achieving the quantum-enhanced sensing, although there are several important concepts associated with criticality, such as long-range correlation, symmetry breaking. In this work, we show that symmetry-breaking alone can drive a quantum-enhanced sensing, even without any gap-to-gapless transition. We analytically demonstrate that the estimation of the superconducting pairing amplitude in the one-dimensional Kitaev model achieves Heisenberg scaling when the system is prepared near a multicritical point and is varied along a gapless critical line, implying symmetry breaking as a standalone metrological resource. Extending our analysis in the realm of simultaneous multiparameter estimation of both the pairing term and the chemical potential, we show that it is possible to obtain L6L^6L6 scaling in a narrow parameter range, but with definite observable consequence, where the quantum advantage is assisted by gap-to-gapless transition as well. Our work thus identifies a new resource for criticality-enhanced quantum sensing, and also suggests multicritical systems as useful platform for multiparameter sensing.