Weight-dependent and weight-independent measures of quantum incompatibility in multiparameter estimation

• URL: http://arxiv.org/abs/2510.18864v1
• Date: Tue, 21 Oct 2025 17:57:52 GMT
• Title: Weight-dependent and weight-independent measures of quantum incompatibility in multiparameter estimation
• Authors: Jiayu He, Gabriele Fazio, Matteo G. A. Paris,
• Abstract summary: Multi quantum estimation faces a fundamental challenge due to the inherent incompatibility of optimal measurements for different parameters.<n>This incompatibility is quantified by the gap between the symmetric logarithmic approximation quantum Cram'er-Rao bound, which is not always attainable, and the derivativeally achievable Holevo bound.<n>This work provides a comprehensive analysis of this gap by introducing and contrasting two scalar measures.
• Score: 0.9379969114114787
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multiparameter quantum estimation faces a fundamental challenge due to the inherent incompatibility of optimal measurements for different parameters, a direct consequence of quantum non-commutativity. This incompatibility is quantified by the gap between the symmetric logarithmic derivative (SLD) quantum Cram\'er-Rao bound, which is not always attainable, and the asymptotically achievable Holevo bound. This work provides a comprehensive analysis of this gap by introducing and contrasting two scalar measures. The first is the weight-independent quantumness measure $R$, which captures the intrinsic incompatibility of the estimation model. The second is a tighter, weight-dependent measure $T[W]$ which explicitly incorporates the cost matrix $W$ assigning relative importance to different parameters. We establish a hierarchy of bounds based on these two measures and derive necessary and sufficient conditions for their saturation. Through analytical and numerical studies of tunable qubit and qutrit models with SU(2) unitary encoding, we demonstrate that the weight-dependent bound $C_{T}[W]$ often provides a significantly tighter approximation to the Holevo bound $C_{H}[W]$ than the $R$-dependent bound, especially in higher-dimensional systems. We also develop an approach based on $C_{T}[W]$ to compute the Holevo bound $C_{H}[W]$ analytically. Our results highlight the critical role of the weight matrix's structure in determining the precision limits of multiparameter quantum metrology.

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)
• Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities [10.43657724071918]
  We propose a universal framework to simultaneously estimate the traces of the $2$nd to the $n$th powers of a reduced density matrix.<n>We develop two algorithms: a purely quantum method and a hybrid quantum-classical approach combining Newton-Girard iteration.<n>We explore various applications including the estimation of nonlinear functions and the representation of entanglement measures.
  arXiv  Detail & Related papers  (2025-07-23T01:41:39Z)
• Achieving the Multi-parameter Quantum Cramér-Rao Bound with Antiunitary Symmetry [18.64293022108985]
  We propose a novel and comprehensive approach to optimize the parameters encoding strategies with the aid of antiunitary symmetry. The results showcase the simultaneous achievement of ultimate precision for multiple parameters without any trade-off.
  arXiv  Detail & Related papers  (2024-11-22T13:37:43Z)
• Dimension matters: precision and incompatibility in multi-parameter quantum estimation models [44.99833362998488]
  We study the role of probe dimension in determining the bounds of precision in quantum estimation problems. We also critically examine the performance of the so-called incompatibility (AI) in characterizing the difference between the Holevo-Cram'er-Rao bound and the Symmetric Logarithmic Derivative (SLD) one.
  arXiv  Detail & Related papers  (2024-03-11T18:59:56Z)
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories [40.772310187078475]
  We propose a novel variational ansatz for the ground-state preparation of the $mathbbZ$ lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve $>!99%$ precision in energy in both the confined and deconfined phase of the $mathbbZ$ LGT.
  arXiv  Detail & Related papers  (2023-08-07T14:23:00Z)
• Analyzing Prospects for Quantum Advantage in Topological Data Analysis [35.423446067065576]
  We analyze and optimize an improved quantum algorithm for topological data analysis. We show that super-quadratic quantum speedups are only possible when targeting a multiplicative error approximation. We argue that quantum circuits with tens of billions of Toffoli can solve seemingly classically intractable instances.
  arXiv  Detail & Related papers  (2022-09-27T17:56:15Z)
• Improving the Accuracy of the Variational Quantum Eigensolver for Molecular Systems by the Explicitly-Correlated Perturbative [2]-R12-Correction [0.0]
  We provide an integration of the universal, perturbative explicitly correlated [2]$_textR12$-correction in the context of the Variational Quantum Eigensolver (VQE) This approach is able to increase the accuracy of the underlying reference method significantly while requiring no additional quantum resources.
  arXiv  Detail & Related papers  (2021-10-13T15:52:01Z)
• 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)
• On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation [62.997667081978825]
  Incompatibility (AI) is a measure which quantifies the difference between the Holevo and the SLD scalar bounds. We show that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than $mu_sf min = 1/(d-1)$.
  arXiv  Detail & Related papers  (2021-07-28T15:16:37Z)
• Quantum Metrology with Coherent Superposition of Two Different Coded Channels [1.430924337853801]
  We show that the Heisenberg limit $1/N$ can be beaten by the coherent superposition without the help of indefinite causal order. We analytically obtain the general form of estimation precision in terms of the quantum Fisher information. Our results can help to construct a high-precision measurement equipment.
  arXiv  Detail & Related papers  (2020-12-03T13:25:16Z)

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.