Quantum Parameter Estimation Uncertainty Relation

• URL: http://arxiv.org/abs/2506.15352v1
• Date: Wed, 18 Jun 2025 11:14:09 GMT
• Title: Quantum Parameter Estimation Uncertainty Relation
• Authors: Bing-Shu Hu, Xiao-Ming Lu,
• Abstract summary: We derive an estimation uncertainty relation that captures the impact of measurement incompatibility and parameter correlation.<n>This uncertainty relation is tight for pure states and completely describes the quantum limit of two- parameter estimation precision.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum multiparameter estimation aims to simultaneously estimate multiple parameters from observing quantum systems and data processing. The complexity of quantum multiparameter estimation arises primarily from measurement incompatibility and parameter correlations. By manipulating the multidimensional parameter space, we derive an estimation uncertainty relation that captures the impact of measurement incompatibility and parameter correlation on quantum two-parameter estimation. This uncertainty relation is tight for pure states and completely describes the quantum limit of two-parameter estimation precision. We also develop an error ellipse method to intuitively illustrate the impact of the uncertainty relation and apply it to the phase-space complex displacement estimation. Our research shows that multiparameter estimation challenges can be effectively addressed by manipulating the geometry of multidimensional parameter space.

Related papers

• Tight tradeoff relation and optimal measurement for multi-parameter quantum estimation [1.0104586293349587]
  This article presents an approach that precisely quantifies the tradeoff resulting from incompatible optimal measurements in quantum estimation.<n>We provide a systematic methodology for constructing optimal measurements that saturate this tight bound in an analytical and structured manner.<n>To demonstrate the power of our findings, we applied our methodology to quantum radar, resulting in a refined Arthurs-Kelly relation.
  arXiv  Detail & Related papers  (2025-04-13T09:10:27Z)
• Randomized measurements for multi-parameter quantum metrology [0.0]
  We show that randomized measurements perform near-optimally when estimating an arbitrary number of parameters in pure states.<n>The near-optimality is also shown in estimating the maximal number of parameters for three types of mixed states that are well-conditioned on its support.
  arXiv  Detail & Related papers  (2025-02-05T19:00:04Z)
• 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)
• Fisher information susceptibility for multiparameter quantum estimation [0.23436632098950458]
  Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit. In quantum metrology, the introduction of the Fisher information measurement noise susceptibility now allows to quantify the robustness of measurement. We provide its mathematical definition in the form of a semidefinite program.
  arXiv  Detail & Related papers  (2023-12-04T16:54:01Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.<n>This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Quantum parameter estimation in a dissipative environment [44.23814225750129]
  We investigate the performance of quantum parameter estimation based on a qubit probe in a dissipative bosonic environment. It is found that (i) the non-Markovianity can effectively boost the estimation performance and (ii) the estimation precision can be improved by introducing a perpendicular probe-environment interaction.
  arXiv  Detail & Related papers  (2021-10-15T02:43:24Z)
• Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation [0.44237366129994526]
  We find a correspondence relationship between the inaccuracy of a measurement for estimating the unknown parameter with the measurement error. For pure quantum states, this tradeoff relation is tight, so it can reveal the true quantum limits on individual estimation errors. We show that our approach can be readily used to derive the tradeoff between the errors of jointly estimating the phase shift and phase diffusion.
  arXiv  Detail & Related papers  (2020-08-20T10:56:45Z)
• Uncertainty and Trade-offs in Quantum Multiparameter Estimation [0.0]
  Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between complementary pieces of information about the system. An uncertainty relation emerges between achievable variances of the different estimators.
  arXiv  Detail & Related papers  (2020-02-14T10:43:40Z)
• Quantum probes for universal gravity corrections [62.997667081978825]
  We review the concept of minimum length and show how it induces a perturbative term appearing in the Hamiltonian of any quantum system. We evaluate the Quantum Fisher Information in order to find the ultimate bounds to the precision of any estimation procedure. Our results show that quantum probes are convenient resources, providing potential enhancement in precision.
  arXiv  Detail & Related papers  (2020-02-13T19:35:07Z)
• In and out of equilibrium quantum metrology with mean-field quantum criticality [68.8204255655161]
  We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level.
  arXiv  Detail & Related papers  (2020-01-09T19:20:42Z)
• Direct estimation of quantum coherence by collective measurements [54.97898890263183]
  We introduce a collective measurement scheme for estimating the amount of coherence in quantum states. Our scheme outperforms other estimation methods based on tomography or adaptive measurements. We show that our method is accessible with today's technology by implementing it experimentally with photons.
  arXiv  Detail & Related papers  (2020-01-06T03:50:42Z)

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.