Hierarchy of saturation conditions for multiparameter quantum metrology bounds

• URL: http://arxiv.org/abs/2602.12097v1
• Date: Thu, 12 Feb 2026 15:50:54 GMT
• Title: Hierarchy of saturation conditions for multiparameter quantum metrology bounds
• Authors: Satoya Imai, Jing Yang, Luca Pezzè,
• Abstract summary: We identify strict gaps between commutativity conditions for unitary parameter-encoding transformations.<n>We show that commutativity alone does not ensure the saturability of the QCR bound once realistic noise produces mixed probe states.
• Score: 3.2237900102017503
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum Cramér-Rao (QCR) bound sets the ultimate local precision limit for unbiased multiparameter estimation. Yet, unlike in the single-parameter case, its saturability is not generally guaranteed and is often assessed through commutativity-based conditions. Here, we resolve the logical hierarchy of these commutativity conditions for unitary parameter-encoding transformations. We identify strict gaps between them, uncover previously assumed but missing implications, and construct explicit counterexamples to characterize the boundaries between distinct classes. In particular, we show that commutativity of the parameter-encoding generators alone does not ensure the saturability of the QCR bound once realistic noise produces mixed probe states. Our results provide a systematic classification of saturability conditions in multiparameter quantum metrology and clarify fundamental precision limits in noisy distributed quantum sensing beyond idealized pure-state settings.

Related papers

• Performance Guarantees for Quantum Neural Estimation of Entropies [31.955071410400947]
  Quantum neural estimators (QNEs) combine classical neural networks with parametrized quantum circuits.<n>We study formal guarantees for QNEs of measured relative entropies in the form of non-asymptotic error risk bounds.<n>Our theory aims to facilitate principled implementation of QNEs for measured relative entropies.
  arXiv  Detail & Related papers  (2025-11-24T16:36:06Z)
• Hybrid Cramér-Rao bound for Quantum Bayes-Point Estimation with Nuisance Parameters [5.247507937352571]
  We develop a hybrid framework for quantum parameter estimation in the presence of nuisance parameters.<n>Within this setting, we introduce the hybrid partial quantum Fisher information matrix (hpQFIM)<n>We illustrate the framework with analytically solvable qubit models and numerical examples.
  arXiv  Detail & Related papers  (2025-10-19T12:34:18Z)
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
  Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application.<n>We analyse the generation of random states in PQCs under restrictions on the qubits connectivities.<n>We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
  arXiv  Detail & Related papers  (2024-05-03T17:32:55Z)
• Saturation of the Multiparameter Quantum Cramér-Rao Bound at the Single-Copy Level with Projective Measurements [0.0]
  It was not known when the quantum Cram'er-Rao bound can be saturated (achieved) when only a single copy of the quantum state is available.<n>In this paper, key structural properties of optimal measurements that saturate the quantum Cram'er-Rao bound are illuminated.
  arXiv  Detail & Related papers  (2024-05-02T17:04:13Z)
• Saturability of the Quantum Cramér-Rao Bound in Multiparameter Quantum Estimation at the Single-Copy Level [0.0]
  The quantum Cram'er-Rao bound (QCRB) is the ultimate lower bound for precision in quantum parameter estimation. This paper establishes necessary and sufficient conditions for saturability of the QCRB in the single-copy setting.
  arXiv  Detail & Related papers  (2024-02-18T12:30:04Z)
• 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)
• Toward Incompatible Quantum Limits on Multiparameter Estimation [4.2043578689409475]
  Heisenberg uncertainty principle prevents optimal measurements for incompatible parameters from being performed jointly. A criterion proposed for multi parameter estimation provides a possible way to beat this curse. A scheme involving high-order Hermite-Gaussian states as probes is proposed for estimating the spatial displacement and angular tilt of light.
  arXiv  Detail & Related papers  (2023-10-11T01:24:03Z)
• Making SGD Parameter-Free [28.088227276891885]
  Our algorithm is conceptually simple, has high-probability guarantees, and is partially adaptive to unknown gradient norms, smoothness, and strong convexity. At the heart of our results is a novel parameter-free certificate for SGD step size choice, and a time-uniform concentration result that assumes no a-priori bounds on SGD iterates.
  arXiv  Detail & Related papers  (2022-05-04T16:29:38Z)
• Incompatibility measures in multi-parameter quantum estimation under hierarchical quantum measurements [4.980960723762946]
  We show an approach to study the incompatibility under general $p$-local measurements. We demonstrate the power of the approach by presenting a hierarchy of analytical bounds on the tradeoff.
  arXiv  Detail & Related papers  (2021-09-13T09:33:47Z)
• Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity [49.66890309455787]
  We introduce the expected co-coercivity condition, explain its benefits, and provide the first last-iterate convergence guarantees of SGDA and SCO. We prove linear convergence of both methods to a neighborhood of the solution when they use constant step-size. Our convergence guarantees hold under the arbitrary sampling paradigm, and we give insights into the complexity of minibatching.
  arXiv  Detail & Related papers  (2021-06-30T18:32:46Z)
• The Variational Method of Moments [65.91730154730905]
  conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables. Motivated by a variational minimax reformulation of OWGMM, we define a very general class of estimators for the conditional moment problem. We provide algorithms for valid statistical inference based on the same kind of variational reformulations.
  arXiv  Detail & Related papers  (2020-12-17T07:21:06Z)

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.