Bayesian Estimation for Bell State Rotations

• URL: http://arxiv.org/abs/2304.05815v1
• Date: Wed, 12 Apr 2023 12:42:29 GMT
• Title: Bayesian Estimation for Bell State Rotations
• Abstract summary: We use a particle filter to estimate the parameters of the rotation from a sequence of Bell state measurements. We demonstrate that the resultant improvement over the optimal single qubit case approaches the $sqrt2$ factor.
• Score: 1.284647943889634
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper explores the effect of three-dimensional rotations on two-qubit Bell states and proposes a Bayesian method for the estimation of the parameters of the rotation. We use a particle filter to estimate the parameters of the rotation from a sequence of Bell state measurements and we demonstrate that the resultant improvement over the optimal single qubit case approaches the $\sqrt{2}$ factor that is consistent with the Heisenberg limit. We also demonstrate how the accuracy of the estimation method is a function of the purity of mixed states.

Related papers

• Smoothness-Based Derandomization of PAC-Bayes Bounds [48.06655334157014]
  We study PAC-Bayes derandomization for smooth loss functions.<n>We show that unbounded passing from the Gibbs predictor to the deterministic predictor at the posterior mean has a precise cost.<n>We specialize the results to linear predictors and smooth neural networks.
  arXiv  Detail & Related papers  (2026-06-17T14:17:44Z)
• Bell State Analysis Provides an Optimal Basis Saturating the Quantum Cramer-Rao in Rotation Sensing [0.0]
  The second-order anti-coherent state of light is known to saturate the Cramer-Rao Bound (QCRB) for rotation sensing around an arbitrary axis.<n>We develop a scheme for extracting the rotation angle for N=4 and N=6 second-order anti-coherent states.
  arXiv  Detail & Related papers  (2026-05-22T18:16:01Z)
• Adaptive quantum metrology with large dynamic range using short one-axis twists [0.0]
  A recently proposed phase estimation scheme approaches the Heisenberg scaling in this global setting.<n>We first observe that the pattern of increase in the squeezing of the probes is applicable even to states with some non-Gaussian features.<n>We show that these states are suitable for use in the phase estimation scheme, and highlight the protocols to achieve $=17/9$ and $53/27$.
  arXiv  Detail & Related papers  (2026-03-14T19:43:39Z)
• Bayesian stepwise estimation of qubit rotations [0.15650076339927835]
  We investigate stepwise estimation (Se) for measuring the two parameters of a unitary qubit rotation.<n>While analysis predicts a precision advantage for SE over joint estimation (JE) in regimes where the quantum Fisher information matrix is near-singular ("sloppy" models)<n>We demonstrate that this advantage is mitigated within a practical Bayesian framework with limited resources.
  arXiv  Detail & Related papers  (2025-12-04T15:26:06Z)
• Preparing the Gutzwiller wave function for attractive SU(3) fermions on a quantum computer [3.2899531615747817]
  We implement the Gutzwiller wave function for attractive SU(3) fermion systems on a quantum computer. We develop and reformulate two complementary methods to perform the sum over auxiliary fields.
  arXiv  Detail & Related papers  (2025-04-25T08:02:34Z)
• Verification of Geometric Robustness of Neural Networks via Piecewise Linear Approximation and Lipschitz Optimisation [57.10353686244835]
  We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for the pixel values by using sampling and linear approximations in combination with branch-and-bound Lipschitz. We show that our proposed implementation resolves up to 32% more verification cases than present approaches.
  arXiv  Detail & Related papers  (2024-08-23T15:02:09Z)
• von Mises Quasi-Processes for Bayesian Circular Regression [57.88921637944379]
  We explore a family of expressive and interpretable distributions over circle-valued random functions. The resulting probability model has connections with continuous spin models in statistical physics. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Markov Chain Monte Carlo sampling.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Bounding the rotating wave approximation for coupled harmonic oscillators [34.82692226532414]
  We study the validity of the rotating wave approximation of an ideal system composed of two harmonic oscillators evolving with a quadratic Hamiltonian and arbitrarily strong interaction.<n>We are able to fully quantify the deviation of arbitrary pure Gaussian states that evolve through different dynamics from a common quantum state.
  arXiv  Detail & Related papers  (2024-03-22T16:51:53Z)
• State Estimation and Control for Stochastic Quantum Dynamics with Homodyne Measurement: Stabilizing Qubits under Uncertainty [1.4811951486536687]
  This paper introduces a Lyapunov-based control approach with homodyne measurement. We study two filtering approaches: (i) the traditional quantum filtering and (ii) a modified version of the extended Kalman filtering.
  arXiv  Detail & Related papers  (2024-03-09T22:29:00Z)
• Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distribution [34.32177951305946]
  Estimating the 3DoF rotation from a single RGB image is a challenging problem.<n>In this paper, we propose a novel rotation Laplace distribution on SO(3).<n>Our method is robust to the disturbance of outliers and enforces much gradient to the low-error region that it can improve.
  arXiv  Detail & Related papers  (2023-05-17T12:31:48Z)
• Minimal-noise estimation of noncommuting rotations of a spin [0.9217021281095907]
  We propose an analogue of $textSU (1,1)$ interferometry to measure rotation of a spin by using two-spin squeezed states. For a specific direction and strength an advantage in sensitivity for all equatorial rotation axes over the classical bound is shown. Our results provide a method for measuring magnetic fields in any direction in the $x$-$y$-plane with the same optimized initial state.
  arXiv  Detail & Related papers  (2023-03-15T13:03:32Z)
• 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)
• Determinant-free fermionic wave function using feed-forward neural networks [0.0]
  We propose a framework for finding the ground state of many-body fermionic systems by using feed-forward neural networks. We show that the accuracy of the approximation can be improved by optimizing the "variance" of the energy simultaneously with the energy itself. These improvements can be applied to other approaches based on variational Monte Carlo methods.
  arXiv  Detail & Related papers  (2021-08-19T11:51:36Z)
• 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)
• Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence [77.06203118175335]
  Variational Inference (VI) is a popular alternative to exact sampling in Bayesian inference. Importance sampling (IS) is often used to fine-tune and de-bias the estimates of approximate Bayesian inference procedures. We propose a novel combination of optimization and sampling techniques for approximate Bayesian inference.
  arXiv  Detail & Related papers  (2021-06-30T11:00:24Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• Regret-Optimal Filtering [57.51328978669528]
  We consider the problem of filtering in linear state-space models through the lens of regret optimization. We formulate a novel criterion for filter design based on the concept of regret between the estimation error energy of a clairvoyant estimator. We show that the regret-optimal estimator can be easily implemented by solving three Riccati equations and a single Lyapunov equation.
  arXiv  Detail & Related papers  (2021-01-25T19:06:52Z)
• Bayesian parameter estimation using Gaussian states and measurements [0.0]
  We consider three paradigmatic estimation schemes in continuous-variable quantum metrology. We investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization.
  arXiv  Detail & Related papers  (2020-09-08T12:54:12Z)
• Path Sample-Analytic Gradient Estimators for Stochastic Binary Networks [78.76880041670904]
  In neural networks with binary activations and or binary weights the training by gradient descent is complicated. We propose a new method for this estimation problem combining sampling and analytic approximation steps. We experimentally show higher accuracy in gradient estimation and demonstrate a more stable and better performing training in deep convolutional models.
  arXiv  Detail & Related papers  (2020-06-04T21:51:21Z)

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.