Holevo Cramér-Rao bound for multi-parameter estimation in nonlinear interferometers

• URL: http://arxiv.org/abs/2502.02855v1
• Date: Wed, 05 Feb 2025 03:17:42 GMT
• Title: Holevo Cramér-Rao bound for multi-parameter estimation in nonlinear interferometers
• Authors: Mengyao Zhou, Hongmei Ma, Liqing Chen, Weiping Zhang, Chun-Hua Yuan,
• Abstract summary: nonlinear interferometers have the potential to surpass the standard quantum limit. We derive the Holevo Cram'er-Rao Bound (HCRB) for the case where both modes undergo displacement estimation. We find that the HCRB equals the result of the dual homodyne measurement, whereas SLD-CRB is not saturable at small squeezed parameters.
• Score: 0.9437165725355702
• License:
• Abstract: Due to the potential of quantum advantage to surpass the standard quantum limit (SQL), the nonlinear interferometers have garnered significant attention from researchers in the field of precision measurement. However, many practical applications require multi-parameter estimation. In this work, we discuss the precision limit of multi-parameter estimation of pure Gaussian states based on nonlinear interferometers, and derive the Holevo Cram\'{e}r-Rao Bound (HCRB) for the case where both modes undergo displacement estimation. Furthermore, we compare our analytical results with the quantum Cram\'er-Rao Bound based on the symmetric logarithmic derivative (SLD-CRB), and with the result of the dual homodyne measurement. Through numerical analysis, we find that the HCRB equals the result of the dual homodyne measurement, whereas SLD-CRB is not saturable at small squeezed parameters. Therefore, this indicates that the HCRB is tight. Additionally, we provide intuitive analysis and visual representation of our numerical results in phase space.

Related papers

• 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)
• Multi-parameter quantum estimation of single- and two-mode pure Gaussian states [0.0]
  We derive the Holevo Cram'er-Rao bound (HCRB) for both displacement and squeezing parameter characterizing single and two-mode squeezed states. In the single-mode scenario, we obtain an analytical bound and find that it degrades monotonically as the squeezing increases. In the two-mode setting, the HCRB improves as the squeezing parameter grows and we show that it can be attained using double-homodyne detection.
  arXiv  Detail & Related papers  (2024-03-06T18:29:17Z)
• Fundamental bounds for parameter estimation with few measurements [0.0]
  We discuss different linear (Barankin-like) conditions that can be imposed on estimators and analyze when these conditions admit an optimal estimator with finite variance. We show that, if the number of imposed conditions is larger than the number of measurement outcomes, there generally does not exist a corresponding estimator with finite variance. We derive an extended Cram'er-Rao bound that is compatible with a finite variance in situations where the Barankin bound is undefined.
  arXiv  Detail & Related papers  (2024-02-22T12:40:08Z)
• 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)
• Towards Convergence Rates for Parameter Estimation in Gaussian-gated Mixture of Experts [40.24720443257405]
  We provide a convergence analysis for maximum likelihood estimation (MLE) in the Gaussian-gated MoE model. Our findings reveal that the MLE has distinct behaviors under two complement settings of location parameters of the Gaussian gating functions. Notably, these behaviors can be characterized by the solvability of two different systems of equations.
  arXiv  Detail & Related papers  (2023-05-12T16:02:19Z)
• Learning Discretized Neural Networks under Ricci Flow [48.47315844022283]
  We study Discretized Neural Networks (DNNs) composed of low-precision weights and activations. DNNs suffer from either infinite or zero gradients due to the non-differentiable discrete function during training.
  arXiv  Detail & Related papers  (2023-02-07T10:51:53Z)
• Two-colour spectrally multimode integrated SU(1,1) interferometer [77.34726150561087]
  We develop and investigate an integrated multimode two-colour SU (1,1) interferometer that operates in a supersensitive mode. By ensuring a proper design of the integrated platform, we suppress dispersion and thereby significantly increase the visibility of the interference pattern. We demonstrate that such an interferometer overcomes the classical phase sensitivity limit for wide parametric gain ranges, when up to $3*104$ photons are generated.
  arXiv  Detail & Related papers  (2022-02-10T13:30:42Z)
• Dual-Frequency Quantum Phase Estimation Mitigates the Spectral Leakage of Quantum Algorithms [76.15799379604898]
  Quantum phase estimation suffers from spectral leakage when the reciprocal of the record length is not an integer multiple of the unknown phase. We propose a dual-frequency estimator, which approaches the Cramer-Rao bound, when multiple samples are available.
  arXiv  Detail & Related papers  (2022-01-23T17:20:34Z)
• Enhanced nonlinear quantum metrology with weakly coupled solitons and particle losses [58.720142291102135]
  We offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg scaling levels. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe. We illustrate that such states are close to the optimal ones even with moderate losses.
  arXiv  Detail & Related papers  (2021-08-07T09:29:23Z)
• Quantum-limited Localisation and Resolution in Three Dimensions [10.824994978916815]
  We determine the ultimate potential of quantum-limited imaging for improving the resolution of a far-field, diffraction-limited approximation. Our results give the upper bounds on certain far-field imaging technology and will find wide applications from microscopy to astrometry.
  arXiv  Detail & Related papers  (2020-12-09T14:44:56Z)
• On the quantumness of multiparameter estimation problems for qubit systems [0.0]
  We consider several estimation problems for qubit systems and evaluate the corresponding quantumness R. R is an upper bound for the renormalized difference between the (asymptotically achievable) Holevo bound and the SLD Cram'er-Rao bound.
  arXiv  Detail & Related papers  (2020-10-23T19:21:50Z)

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.