Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2608.01831

Symmetry-Projected Compatible Multiparameter Quantum Sensing

G. R. Jin, Z. Y. Zhou, W. Yang

quant-phphysics.atom-phphysics.opticsSubmitted Aug 3, 2026• Announced Aug 4, 2026• 0 citations
v1 · Aug 3, 2026v2 · Aug 7, 2026
arXivHTMLPDF

Abstract

We establish a general symmetry-projection framework for multiparameter quantum sensing. Decomposing encoding generators into subspace-preserving and subspace-changing components relative to a symmetry sector identically eliminates all cross-sector elements of the quantum Fisher information matrix (QFIM) and the mean symmetric logarithmic derivative (SLD) commutator matrix. When projected subspace-changing generators act as a scalar within the occupied subspace, the corresponding QFIM block reduces to four times the symmetrized covariance matrix, regardless of probe state purity. For parity-protected collective $\mathrm{SU}(2)$ spin systems, this renders the transverse QFIM directly certifiable via spin fluctuations, with the optimal axis aligned with the anti-squeezed quadrature. Applied to a dissipative one-axis-twisting system, our framework reveals that highly mixed transient states can exhibit nearly balanced, Heisenberg-scaled QFIM components for transverse--longitudinal parameter pairs $(θ_y,θ_z)$ over a broad time window. Furthermore, while the steady state retains an isotropic transverse QFIM scaling as $N^2/3$, weak compatibility for transverse parameter pairs $(θ_x,θ_y)$ exhibits a sharp parity dependence---failing for odd $N$ but restored for even $N$. The resulting symmetry protection eliminates the Uhlmann curvature for transverse--longitudinal pairs, enabling simultaneous saturation of the multi-parameter quantum Cramér-Rao bound in the asymptotic limit.

Comments
6.2 pages, 1 figures

Related papers

Simultaneous Heisenberg-Limited Multiparameter Metrology via Indefinite Evolution

Hang Xu, Tailong Xiao, Ze Zheng +4 more

Quantum metrology achieves Heisenberg-limited precision in single-parameter estimation, but its multiparameter extension is fundamentally constrained by both parameter-encoding and measurement incompatibility. Noncommuting signal generators may cause incompatible parameter-encoding, preventing the quantum Fisher information matrix from simultaneously achieving the Heisenberg scale for all parameters. Due to incompatible optimal measurements, the classical Fisher information matrix represents the practical attainable precision. Here, we introduce a multiparameter metrology framework based on indefinite evolution (IE), in which different control operations and signal reversal are placed in a coherent superposition. For a single-qubit probe with mutually orthogonal signal generators, IE enables compatible parameter encoding and optimal measurement without the signal reversal. For parallel generators, where only signal reversal realized by its generator is available, IE can achieve the same performance. We further extend this mechanism to noisy, many-body, and high-dimensional probes, and establish general conditions for achieving the simultaneous Heisenberg-limit. In contrast, definite evolution cannot achieve the same performance under compatible optimal measurements, even when signal reversal is available. Our results identify IE as an operational resource for overcoming multiparameter incompatibility and open a route toward attainable Heisenberg-limited sensing in interferometric platforms.

quant-pharXiv:2608.10490•Aug 12, 2026•0 citations

Quantifying Uhlmann curvature from Yang-Mills action and its implications in quantum multiparameter estimation

Yi-Lin Ge, Bing-Shu Hu, Ling-Yun Deng +1 more

The geometry of quantum states has profound implications in quantum multiparameter estimation. While the Riemannian structure of quantum state space is well understood, the full understanding of the curvature structure of mixed quantum states is still an open problem. Inspired by the Yang-Mills action in non-Abelian gauge theory, we propose a scalar quantifying the Uhlmann curvature and establish its connection to the measurement incompatibility in quantum multiparameter estimation problems. We show that this curvature measure is gauge invariant, reparametrization invariant, and vanishes if and only if the Uhlmann curvature vanishes. We also explicitly calculate the Uhlmann curvature for the joint estimation of phase and phase diffusion as an example.

quant-pharXiv:2604.15752•Apr 20, 2026•0 citations

Quantum-enhanced single and multiparameter metrology in qutrit ensembles by generalized twisting dynamics

Deep Datta, Sayam Chakraborty, John Drew Wilson +2 more

Quantum-enhanced sensing with atomic ensembles has predominantly focused on qubit-based protocols, despite the growing ability of many experimental platforms to coherently control and entangle multi-level systems. Here, we investigate quantum-enhanced sensing with qutrit ensembles by introducing three experimentally feasible qutrit generalisations of the one-axis twisting (OAT) model that involve entangling operations only between two levels, while the third level primarily acts as a spectator. We characterize the metrological utility of the dynamically generated states using the quantum Fisher information toolbox. We find numerically that all three models offer considerable freedom in encoding direction for quantum-enhanced sensing, with up to 6 out of 8 possible directions exhibit near-Heisenberg scaling after a short evolution time. We discuss experimental access to this enhanced metrological precision via effective time-reversal protocols. Furthermore, we examine the practical issues of estimation ambiguity and local dissipation, and show that they can be largely overcome by optimizing the sensor operating point. Finally, we show that the measurement incompatibility in estimating multiple parameters simultaneously encoded in different directions with near-Heisenberg scaling of precision is suppressed at the zero operating point as the system size increases. In the process, we find that one of the models enables near-Heisenberg scaling metrology with a pair of commuting generators, a possibility that arises from the $su(3)$ algebra and is thus absent in qubit-ensemble based sensors of collective $SU(2)$ rotations.

quant-pharXiv:2608.26630•Aug 28, 2026•0 citations

Single-Ensemble Multiparameter Squeezing with Qudits

Xiaoshui Lin, Chunlei Qu, Chong Zu +1 more

Conventional spin squeezing enhances a single sensing channel. Here, we show how internal qudit levels enable simultaneous multiparameter squeezing within one ensemble. In two-component magnetometry, a qutrit sensor provides two orthogonal and weakly compatible channels. A collective twisting interaction squeezes both responses while preserving joint attainability of the ultimate sensitivity. The sensing gain is quantified by using a matrix generalization of the Wineland sensitivity that retains both noise correlations and cross-channel response. An interaction-based echo amplifies the signal to overcome noise from a fixed local joint readout, yielding a simulated $13~\mathrm{dB}$ gain over the product-state standard quantum limit for $N=128$ qutrits. More generally, we use the single-site quantum Fisher information matrix to select reference states and channel quadratures for prescribed sensing tasks. The tangent geometry permits at most $d-1$ independent, weakly compatible channels around a common pure reference state for a $d$-level sensor. Our work provides a constructive task-to-protocol map for multiparameter squeezing in a single qudit ensemble.

quant-pharXiv:2605.26377•May 27, 2026•0 citations

Multiparameter Gaussian quantum metrology

Rosanna Nichols, Pietro Liuzzo-Scorpo, Paul A. Knott +1 more

We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cram\'er-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfill the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.

arXiv:1711.09132•Physical Review A•Jul 11, 2018•130 citations

Multi-Parameter Multi-Critical Metrology of the Dicke Model

Luca Previdi, Yilun Xu, Qiongyi He +1 more

Critical quantum metrology exploits the hypersensitivity of quantum systems near phase transitions to achieve enhanced precision in parameter estimation. While single-parameter estimation near critical points is well established, the simultaneous estimation of multiple parameters, which is essential for practical sensing applications, remains challenging. This difficulty arises from sloppiness, a phenomenon that typically renders the quantum Fisher information matrix (QFIM) singular or nearly singular. In this work, we demonstrate that multiparameter critical metrology is not only feasible but can also retain divergent precision scaling, provided one accepts a trade-off in the scaling exponent. Using the ground state of the single-cavity Dicke model (DM), we show that two Hamiltonian parameters can be simultaneously estimated with a scalar variance bound scaling as the square root of the critical parameter. This overcomes the inherent sloppiness by leveraging higher-order contributions to the QFIM. To recover the optimal quadratic scaling, we introduce the Dicke dimer (DD) with photon hopping. In this extended model, a triple point in the phase diagram enables the simultaneous closure of two excitation gaps, which effectively increases the rank of the QFIM and restores the ideal single-parameter scaling for specific parameter pairs. Furthermore, we extend our analysis to dissipative settings subject to photon loss. Finally, we establish a connection between the derived critical scalings and the fundamental state preparation time, providing a unified framework to operationally compare different sensing strategies. Our results demonstrate that critical quantum metrology can be made robust against dissipation and scalable to multiparameter scenarios, paving the way for practical quantum sensors operating near phase transitions.

quant-pharXiv:2603.03451•Mar 5, 2026•0 citations
We establish a general symmetry-projection framework for multiparameter quantum sensing. Decomposing encoding generators into subspace-preserving and subspace-changing components relative to a symmetry sector identically eliminates all cross-sector elements of the quantum Fisher information matrix (QFIM) and the mean symmetric logarithmic derivative (SLD) commutator matrix. When projected subspace-changing generators act as a scalar within the occupied subspace, the corresponding QFIM block reduces to four times the symmetrized covariance matrix, regardless of probe state purity. For parity-protected collective SU(2)\mathrm{SU}(2)SU(2) spin systems, this renders the transverse QFIM directly certifiable via spin fluctuations, with the optimal axis aligned with the anti-squeezed quadrature. Applied to a dissipative one-axis-twisting system, our framework reveals that highly mixed transient states can exhibit nearly balanced, Heisenberg-scaled QFIM components for transverse--longitudinal parameter pairs (θy,θz)(θ_y,θ_z)(θy​,θz​) over a broad time window. Furthermore, while the steady state retains an isotropic transverse QFIM scaling as N2/3N^2/3N2/3, weak compatibility for transverse parameter pairs (θx,θy)(θ_x,θ_y)(θx​,θy​) exhibits a sharp parity dependence---failing for odd NNN but restored for even NNN. The resulting symmetry protection eliminates the Uhlmann curvature for transverse--longitudinal pairs, enabling simultaneous saturation of the multi-parameter quantum Cramér-Rao bound in the asymptotic limit.
Quantum metrology achieves Heisenberg-limited precision in single-parameter estimation, but its multiparameter extension is fundamentally constrained by both parameter-encoding and measurement incompatibility. Noncommuting signal generators may cause incompatible parameter-encoding, preventing the quantum Fisher information matrix from simultaneously achieving the Heisenberg scale for all parameters. Due to incompatible optimal measurements, the classical Fisher information matrix represents the practical attainable precision. Here, we introduce a multiparameter metrology framework based on indefinite evolution (IE), in which different control operations and signal reversal are placed in a coherent superposition. For a single-qubit probe with mutually orthogonal signal generators, IE enables compatible parameter encoding and optimal measurement without the signal reversal. For parallel generators, where only signal reversal realized by its generator is available, IE can achieve the same performance. We further extend this mechanism to noisy, many-body, and high-dimensional probes, and establish general conditions for achieving the simultaneous Heisenberg-limit. In contrast, definite evolution cannot achieve the same performance under compatible optimal measurements, even when signal reversal is available. Our results identify IE as an operational resource for overcoming multiparameter incompatibility and open a route toward attainable Heisenberg-limited sensing in interferometric platforms.
The geometry of quantum states has profound implications in quantum multiparameter estimation. While the Riemannian structure of quantum state space is well understood, the full understanding of the curvature structure of mixed quantum states is still an open problem. Inspired by the Yang-Mills action in non-Abelian gauge theory, we propose a scalar quantifying the Uhlmann curvature and establish its connection to the measurement incompatibility in quantum multiparameter estimation problems. We show that this curvature measure is gauge invariant, reparametrization invariant, and vanishes if and only if the Uhlmann curvature vanishes. We also explicitly calculate the Uhlmann curvature for the joint estimation of phase and phase diffusion as an example.
Quantum-enhanced sensing with atomic ensembles has predominantly focused on qubit-based protocols, despite the growing ability of many experimental platforms to coherently control and entangle multi-level systems. Here, we investigate quantum-enhanced sensing with qutrit ensembles by introducing three experimentally feasible qutrit generalisations of the one-axis twisting (OAT) model that involve entangling operations only between two levels, while the third level primarily acts as a spectator. We characterize the metrological utility of the dynamically generated states using the quantum Fisher information toolbox. We find numerically that all three models offer considerable freedom in encoding direction for quantum-enhanced sensing, with up to 6 out of 8 possible directions exhibit near-Heisenberg scaling after a short evolution time. We discuss experimental access to this enhanced metrological precision via effective time-reversal protocols. Furthermore, we examine the practical issues of estimation ambiguity and local dissipation, and show that they can be largely overcome by optimizing the sensor operating point. Finally, we show that the measurement incompatibility in estimating multiple parameters simultaneously encoded in different directions with near-Heisenberg scaling of precision is suppressed at the zero operating point as the system size increases. In the process, we find that one of the models enables near-Heisenberg scaling metrology with a pair of commuting generators, a possibility that arises from the su(3)su(3)su(3) algebra and is thus absent in qubit-ensemble based sensors of collective SU(2)SU(2)SU(2) rotations.
Conventional spin squeezing enhances a single sensing channel. Here, we show how internal qudit levels enable simultaneous multiparameter squeezing within one ensemble. In two-component magnetometry, a qutrit sensor provides two orthogonal and weakly compatible channels. A collective twisting interaction squeezes both responses while preserving joint attainability of the ultimate sensitivity. The sensing gain is quantified by using a matrix generalization of the Wineland sensitivity that retains both noise correlations and cross-channel response. An interaction-based echo amplifies the signal to overcome noise from a fixed local joint readout, yielding a simulated 13 dB13~\mathrm{dB}13 dB gain over the product-state standard quantum limit for N=128N=128N=128 qutrits. More generally, we use the single-site quantum Fisher information matrix to select reference states and channel quadratures for prescribed sensing tasks. The tangent geometry permits at most d−1d-1d−1 independent, weakly compatible channels around a common pure reference state for a ddd-level sensor. Our work provides a constructive task-to-protocol map for multiparameter squeezing in a single qudit ensemble.
We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cram\'er-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfill the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.
Critical quantum metrology exploits the hypersensitivity of quantum systems near phase transitions to achieve enhanced precision in parameter estimation. While single-parameter estimation near critical points is well established, the simultaneous estimation of multiple parameters, which is essential for practical sensing applications, remains challenging. This difficulty arises from sloppiness, a phenomenon that typically renders the quantum Fisher information matrix (QFIM) singular or nearly singular. In this work, we demonstrate that multiparameter critical metrology is not only feasible but can also retain divergent precision scaling, provided one accepts a trade-off in the scaling exponent. Using the ground state of the single-cavity Dicke model (DM), we show that two Hamiltonian parameters can be simultaneously estimated with a scalar variance bound scaling as the square root of the critical parameter. This overcomes the inherent sloppiness by leveraging higher-order contributions to the QFIM. To recover the optimal quadratic scaling, we introduce the Dicke dimer (DD) with photon hopping. In this extended model, a triple point in the phase diagram enables the simultaneous closure of two excitation gaps, which effectively increases the rank of the QFIM and restores the ideal single-parameter scaling for specific parameter pairs. Furthermore, we extend our analysis to dissipative settings subject to photon loss. Finally, we establish a connection between the derived critical scalings and the fundamental state preparation time, providing a unified framework to operationally compare different sensing strategies. Our results demonstrate that critical quantum metrology can be made robust against dissipation and scalable to multiparameter scenarios, paving the way for practical quantum sensors operating near phase transitions.