Characterizing resources for multiparameter estimation of SU(2) and SU(1,1) unitaries

• URL: http://arxiv.org/abs/2412.19119v2
• Date: Mon, 27 Jan 2025 12:40:25 GMT
• Title: Characterizing resources for multiparameter estimation of SU(2) and SU(1,1) unitaries
• Authors: Shaowei Du, Shuheng Liu, Frank E. S. Steinhoff, Giuseppe Vitagliano,
• Abstract summary: We investigate the scaling of the precision in a pragmatic framework where the estimation is performed via the so-called method of moments. We consider optimal or close-to-optimal initial states, that can be obtained by maximizing the quantum Fisher information matrix. We find that in our context with limited resources accessible, the twin-Fock state emerges as the best probe state.
• Score: 1.8749305679160366
• License:
• Abstract: We follow recent works analyzing precision bounds to the estimation of multiple parameters generated by a unitary evolution with non-commuting Hamiltonians that form a closed algebra. We consider the $3$-parameter estimation of SU(2) and SU(1,1) unitaries and investigate the scaling of the precision in a pragmatic framework where the estimation is performed via the so-called method of moments, consisting in the estimation of phases via expectation values of time-evolved observables, which we restrict to be the first two moments of the Hamiltonian generators. We consider optimal or close-to-optimal initial states, that can be obtained by maximizing the quantum Fisher information matrix, and analyze the maximal precision achievable from measuring only the first two moments of the generators. As a result, we find that in our context with limited resources accessible, the twin-Fock state emerges as the best probe state, that allows the estimation of two out of the three parameters with Heisenberg precision scaling. Moreover, in other practical scenarios with less limitations we identify useful probe states that can in principle achieve Heisenberg scaling for the three parameters considered.

Related papers

• 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)
• Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations [0.0]
  A major task in quantum sensing is to design the optimal protocol, i.e., the most precise one. Here, we focus on the single-shot Bayesian setting, where the goal is to find the optimal initial state of the probe. We leverage the formalism of higher-order operations to develop a method that finds a protocol that is close to the optimal one with arbitrary precision.
  arXiv  Detail & Related papers  (2023-11-02T18:00:36Z)
• Parameter estimation with limited access of measurements [0.12102521201635405]
  We present a theoretical framework to explore the parameter estimation with limited access of measurements. We analyze the effect of non-optimal measurement on the estimation precision. We show that the minimum Euclidean distance between an observable and the optimal ones is analyzed and the results show that the observable closed to the optimal ones better.
  arXiv  Detail & Related papers  (2023-10-06T05:34:32Z)
• Quantum multiparameter estimation with graph states [6.152619905686453]
  In the SU(2) dynamics, it is especially significant to achieve a simultaneous optimal multi parameter estimation. We propose a simultaneous multi parameter estimation scheme that investigates evolution in SU(N) dynamics. We prove that the graph state is the optimal state of quantum metrology, a set of optimal measurement basic can be found, and the precision limit of multi parameter estimation can attain the quantum Cram'er-Rao bound.
  arXiv  Detail & Related papers  (2023-06-05T00:50:24Z)
• Multiparameter estimation of continuous-time Quantum Walk Hamiltonians through Machine Learning [0.0]
  We describe a continuous-time quantum walk over a line graph with $n$-neighbour interactions using a deep neural network model. We find that the neural network acts as a nearly optimal estimator both when the estimation of two or three parameters is performed.
  arXiv  Detail & Related papers  (2022-11-10T15:03:21Z)
• Structural aspects of FRG in quantum tunnelling computations [68.8204255655161]
  We probe both the unidimensional quartic harmonic oscillator and the double well potential. Two partial differential equations for the potential V_k(varphi) and the wave function renormalization Z_k(varphi) are studied.
  arXiv  Detail & Related papers  (2022-06-14T15:23:25Z)
• Quantum probes for the characterization of nonlinear media [50.591267188664666]
  We investigate how squeezed probes may improve individual and joint estimation of the nonlinear coupling $tildelambda$ and of the nonlinearity order $zeta$. We conclude that quantum probes represent a resource to enhance precision in the characterization of nonlinear media, and foresee potential applications with current technology.
  arXiv  Detail & Related papers  (2021-09-16T15:40:36Z)
• Mean-Square Analysis with An Application to Optimal Dimension Dependence of Langevin Monte Carlo [60.785586069299356]
  This work provides a general framework for the non-asymotic analysis of sampling error in 2-Wasserstein distance. Our theoretical analysis is further validated by numerical experiments.
  arXiv  Detail & Related papers  (2021-09-08T18:00:05Z)
• Two-parameter estimation with three-mode NOON state in a symmetric three-well system [0.0]
  The sensitivity of this estimation scheme is studied by comparing quantum and classical Fisher information matrices. The precision of this estimation scheme behaves the Heisenberg scaling under the optimal measurement.
  arXiv  Detail & Related papers  (2021-07-06T08:13:23Z)
• Fundamental Limits of Ridge-Regularized Empirical Risk Minimization in High Dimensions [41.7567932118769]
  Empirical Risk Minimization algorithms are widely used in a variety of estimation and prediction tasks. In this paper, we characterize for the first time the fundamental limits on the statistical accuracy of convex ERM for inference.
  arXiv  Detail & Related papers  (2020-06-16T04:27:38Z)
• 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)

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.