Optimal Quantum Estimation with Stabilizer-Based Local Measurements

• URL: http://arxiv.org/abs/2508.07150v1
• Date: Sun, 10 Aug 2025 02:51:07 GMT
• Title: Optimal Quantum Estimation with Stabilizer-Based Local Measurements
• Abstract summary: We present a sufficient criterion for metrological schemes to saturate the quantum Cram'er-Rao bound (QCRB) using local measurements.<n>A family of graph states is identified as probe states that achieve suboptimal precision scaling.<n>We construct several subspaces of probe states that not only saturate the QCRB with local measurements but also maintain approximately invariant precision scaling.
• Score: 3.9436039611833964
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A central challenge in quantum metrology is to identify optimal protocols under measurement constraints that reflect realistic experimental conditions, e.g., local measurements in multipartite scenarios. Here, we present a sufficient criterion for metrological schemes to saturate the quantum Cram\'er-Rao bound (QCRB) using local measurements, based on stabilizer formalism. In ideal settings, we show that graph states always admit local estimation protocols with an optimal estimation precision determined only by the underlying graph structure. A family of graph states is identified as probe states that achieve suboptimal precision scaling. In noisy environments, we construct several subspaces of probe states (mixed in general) that not only saturate the QCRB with local measurements but also maintain approximately invariant precision scaling. These subspaces offer multiple metrological advantages, including high precision, partial noise resilience, and noise-correcting capability prior to parameter encoding. Under dephasing noise, they exhibit markedly better performance than Greenberger-Horne-Zeilinger states. Our results advance the framework for local-measurement quantum metrology, achieving a robust trade-off between precision and noise tolerance.

Related papers

• Characterizing Heterogeneous Rates in Finite Mixture Estimation via Partial Optimal Transport [88.55403215843967]
  Voronoi-based partial optimal transport (VPOT) for obtaining refined local and global convergence guarantees for the maximum likelihood estimator of the mixing measure.<n>Results hold in arbitrary fixed dimension without requiring mixing proportions to be uniformly bounded away from zero or prior knowledge of the true number of mixture components.
  arXiv  Detail & Related papers  (2026-09-15T04:32:53Z)
• Scalable Lindblad Noise Learning via Stochastic Tensor-Network Simulation [48.887627688666974]
  Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies.<n>Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a simulation method, the Jump Method (TJM)<n>We demonstrate the approach on two noise models in the Ising model, in which independent dissipation rates are learned for each site up to $N_mathrmsite=16$.<n>This combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices.
  arXiv  Detail & Related papers  (2026-08-25T15:07:11Z)
• Adaptive Reconstruction of Bosonic Quantum States [1.889677290907544]
  Bosonic quantum systems provide a hardware-efficient platform for quantum information processing.<n>Existing approaches estimate the fidelity with respect to a single target state.<n>We introduce an adaptive reconstruction technique that estimates the fidelity with respect to a family of bosonic states.
  arXiv  Detail & Related papers  (2026-08-03T10:46:53Z)
• From Atoms to Entropy: Optimal Noise Allocation for Diffusion Training in the Convex Regime [52.459513910242485]
  We develop a general statistical framework for studying optimal noise-level allocation in diffusion training.<n>We show that the optimized training schedule admits an atomic minimizer, concentrated on finitely many noise levels.<n>We then evaluate the entropic schedule in larger-scale experiments, where full schedule optimization is currently intractable.
  arXiv  Detail & Related papers  (2026-07-10T20:59:06Z)
• Designing Preconditioners for SGD: Local Conditioning, Noise Floors, and Basin Stability [38.75338802679837]
  Gradient Descent (SGD) often slows in the late stage of training due to anisotropic curvature and gradient noise.<n>We analyze SGD in geometry induced by a symmetric positive matrix $mathbfM$, deriving bounds in which both the convergence rate and the noise floor areBounded by $mathbfM$-dependent quantities.<n>Experiments on a diagnostic and three SciML benchmarks validate the predicted-floor behavior.
  arXiv  Detail & Related papers  (2025-11-24T21:24:40Z)
• Practical robust Bayesian spin-squeezing-enhanced quantum sensing under noises [4.276364453866415]
  We present an adaptive Bayesian quantum estimation protocol that achieves optimal measurement precision with spin-squeezed states under noises.<n>Our protocol can be applied to various scenarios, such as quantum gravimeters and atomic clocks, achieving precision enhancement over conventional fitting methods under noises.
  arXiv  Detail & Related papers  (2025-09-10T06:40:35Z)
• Extending the dynamic range in quantum frequency estimation with sequential weak measurements [0.10923877073891443]
  We study schemes to extend the dynamic range and overcome phase slip noise through weak measurements with ancilla qubits.<n>We find optimal weak measurements protocols: we identify optimal measurement strength for any given optical number of atoms.<n>Then we combine weak and projective measurements to construct a protocol that saturates the noiseless precision limits, and outperforms previously proposed methods for phase slip noise suppression.
  arXiv  Detail & Related papers  (2025-09-01T13:42:17Z)
• Heisenberg-limited Bayesian phase estimation with low-depth digital quantum circuits [0.0]
  We develop and analyze a scheme that achieves near-optimal precision up to a constant overhead for Bayesian phase estimation. We show that the proposed scheme outperforms known schemes in the literature that utilize a similar set of initial states. We also propose an efficient phase unwinding protocol to extend the dynamic range of the proposed scheme.
  arXiv  Detail & Related papers  (2024-07-08T14:59:16Z)
• Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networks [36.136619420474766]
  parametric physics-informed neural networks (PINNs) for model calibration from full-field displacement data are investigated.<n>Due to the fast evaluation of PINNs, calibration can be performed in near real-time.
  arXiv  Detail & Related papers  (2024-05-28T16:02:11Z)
• Finding the optimal probe state for multiparameter quantum metrology using conic programming [61.98670278625053]
  We present a conic programming framework that allows us to determine the optimal probe state for the corresponding precision bounds. We also apply our theory to analyze the canonical field sensing problem using entangled quantum probe states.
  arXiv  Detail & Related papers  (2024-01-11T12:47:29Z)
• Robust and efficient verification of graph states in blind measurement-based quantum computation [52.70359447203418]
  Blind quantum computation (BQC) is a secure quantum computation method that protects the privacy of clients. It is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension.
  arXiv  Detail & Related papers  (2023-05-18T06:24:45Z)
• Optimal Scaling for Locally Balanced Proposals in Discrete Spaces [65.14092237705476]
  We show that efficiency of Metropolis-Hastings (M-H) algorithms in discrete spaces can be characterized by an acceptance rate that is independent of the target distribution. Knowledge of the optimal acceptance rate allows one to automatically tune the neighborhood size of a proposal distribution in a discrete space, directly analogous to step-size control in continuous spaces.
  arXiv  Detail & Related papers  (2022-09-16T22:09:53Z)
• Local Stochastic Factored Gradient Descent for Distributed Quantum State Tomography [10.623470454359431]
  Local Factored Gradient Descent (Local SFGD) Quantum State Tomography (QST) protocol. Local SFGD converges locally to a small neighborhood of the global at a linear rate with a constant step size.
  arXiv  Detail & Related papers  (2022-03-22T10:03:16Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• Quantum metrology with one auxiliary particle in a correlated bath and its quantum simulation [1.0118253437732931]
  The precision of parameter estimation with entangled probes is even lower than that of the unentangled ones in a correlated environment. We propose a measurement scheme with only one auxiliary qubit, which can selectively offset the impact of environmental noise.
  arXiv  Detail & Related papers  (2021-05-21T10:24:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.