Bayesian quantum phase estimation with fixed photon states

• URL: http://arxiv.org/abs/2308.01293v2
• Date: Mon, 14 Oct 2024 23:30:49 GMT
• Title: Bayesian quantum phase estimation with fixed photon states
• Authors: Boyu Zhou, Saikat Guha, Christos N. Gagatsos,
• Abstract summary: We consider a two-mode bosonic state with fixed photon number $n in mathbbN$, whose upper and lower modes pick up a phase $phi$ and $-phi$ respectively. We compute the optimal Fock coefficients of the input state, such that the mean square error (MSE) for estimating $phi$ is minimized.
• Score: 5.287546642230383
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a two-mode bosonic state with fixed photon number $n \in \mathbb{N}$, whose upper and lower modes pick up a phase $\phi$ and $-\phi$ respectively. We compute the optimal Fock coefficients of the input state, such that the mean square error (MSE) for estimating $\phi$ is minimized while the minimum MSE is always attainable by a measurement. Our setting is Bayesian, i.e., we consider $\phi$ to be a random variable that follows a prior probability distribution function (PDF). Initially, we consider the flat prior PDF and we discuss the well-known fact that the MSE is not an informative tool for estimating a phase when the variance of the prior PDF is large. Therefore, we move on to study truncated versions of the flat prior in both single-shot and adaptive approaches. For our adaptive technique we consider $n=1$ and truncated prior PDFs. Each subsequent step utilizes as prior PDF the posterior probability of the previous step and at the same time we update the optimal state and optimal measurement.

Related papers

• Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models [5.939858158928473]
  Diffusion probabilistic models generate samples by learning to reverse a noise-injection process that transforms data into noise.<n>Reformulating this reverse process as a deterministic probability flow ordinary differential equation (ODE) enables efficient sampling using high-order solvers.<n>Since the score function is typically approximated by a neural network, analyzing the interaction between its regularity, approximation error, and numerical integration error is key to understanding the overall sampling accuracy.
  arXiv  Detail & Related papers  (2025-06-16T03:09:25Z)
• Adaptive stable distribution and Hurst exponent by method of moments moving estimator for nonstationary time series [0.49728186750345144]
  We will focus on novel more agnostic approach: moving estimator, which estimates parameters separately for every time.<n>We will show its applications for alpha-Stable distribution, which also influences Hurst exponent, hence can be used for its adaptive estimation.
  arXiv  Detail & Related papers  (2025-05-20T08:36:49Z)
• From Continual Learning to SGD and Back: Better Rates for Continual Linear Models [50.11453013647086]
  We analyze the forgetting, i.e., loss on previously seen tasks, after $k$ iterations.<n>We develop novel last-iterate upper bounds in the realizable least squares setup.<n>We prove for the first time that randomization alone, with no task repetition, can prevent catastrophic in sufficiently long task sequences.
  arXiv  Detail & Related papers  (2025-04-06T18:39:45Z)
• Active Subsampling for Measurement-Constrained M-Estimation of Individualized Thresholds with High-Dimensional Data [3.1138411427556445]
  In the measurement-constrained problems, despite the availability of large datasets, we may be only affordable to observe the labels on a small portion of the large dataset. This poses a critical question that which data points are most beneficial to label given a budget constraint. In this paper, we focus on the estimation of the optimal individualized threshold in a measurement-constrained M-estimation framework.
  arXiv  Detail & Related papers  (2024-11-21T00:21:17Z)
• Variance Reduction for the Independent Metropolis Sampler [11.074080383657453]
  We prove that if $pi$ is close enough under KL divergence to another density $q$, an independent sampler that obtains samples from $pi$ achieves smaller variance than i.i.d. sampling from $pi$. We propose an adaptive independent Metropolis algorithm that adapts the proposal density such that its KL divergence with the target is being reduced.
  arXiv  Detail & Related papers  (2024-06-25T16:38:53Z)
• Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions [11.222970035173372]
  kernel-based score estimator achieves an optimal mean square error of $widetildeOleft(n-1 t-fracd+22(tfracd2 vee 1)right) We show that a kernel-based score estimator achieves an optimal mean square error of $widetildeOleft(n-1/2 t-fracd4right)$ upper bound for the total variation error of the distribution of the sample generated by the diffusion model under a mere sub-Gaussian
  arXiv  Detail & Related papers  (2024-02-23T20:51:31Z)
• Towards Optimal Statistical Watermarking [95.46650092476372]
  We study statistical watermarking by formulating it as a hypothesis testing problem. Key to our formulation is a coupling of the output tokens and the rejection region. We characterize the Uniformly Most Powerful (UMP) watermark in the general hypothesis testing setting.
  arXiv  Detail & Related papers  (2023-12-13T06:57:00Z)
• A Specialized Semismooth Newton Method for Kernel-Based Optimal Transport [92.96250725599958]
  Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. We show that our SSN method achieves a global convergence rate of $O (1/sqrtk)$, and a local quadratic convergence rate under standard regularity conditions.
  arXiv  Detail & Related papers  (2023-10-21T18:48:45Z)
• Bayesian minimum mean square error for transmissivity sensing [5.348876409230946]
  We address the problem of estimating the transmissivity of the pure-loss channel from the Bayesian point of view. We employ methods to compute the Bayesian minimum mean square error (MMSE) We study the performance of photon-counting, which is a sub-optimal yet practical measurement.
  arXiv  Detail & Related papers  (2023-04-12T00:01:28Z)
• Estimating the minimizer and the minimum value of a regression function under passive design [72.85024381807466]
  We propose a new method for estimating the minimizer $boldsymbolx*$ and the minimum value $f*$ of a smooth and strongly convex regression function $f$. We derive non-asymptotic upper bounds for the quadratic risk and optimization error of $boldsymbolz_n$, and for the risk of estimating $f*$.
  arXiv  Detail & Related papers  (2022-11-29T18:38:40Z)
• (Nearly) Optimal Private Linear Regression via Adaptive Clipping [22.639650869444395]
  We study the problem of differentially private linear regression where each data point is sampled from a fixed sub-Gaussian style distribution. We propose and analyze a one-pass mini-batch gradient descent method (DP-AMBSSGD) where points in each iteration are sampled without replacement.
  arXiv  Detail & Related papers  (2022-07-11T08:04:46Z)
• Conditionally Calibrated Predictive Distributions by Probability-Probability Map: Application to Galaxy Redshift Estimation and Probabilistic Forecasting [4.186140302617659]
  Uncertainty is crucial for assessing the predictive ability of AI algorithms. We propose textttCal-PIT, a method that addresses both PD diagnostics and recalibration. We benchmark our corrected prediction bands against oracle bands and state-of-the-art predictive inference algorithms.
  arXiv  Detail & Related papers  (2022-05-29T03:52:44Z)
• A Momentum-Assisted Single-Timescale Stochastic Approximation Algorithm for Bilevel Optimization [112.59170319105971]
  We propose a new algorithm -- the Momentum- Single-timescale Approximation (MSTSA) -- for tackling problems. MSTSA allows us to control the error in iterations due to inaccurate solution to the lower level subproblem.
  arXiv  Detail & Related papers  (2021-02-15T07:10:33Z)
• Debiasing Distributed Second Order Optimization with Surrogate Sketching and Scaled Regularization [101.5159744660701]
  In distributed second order optimization, a standard strategy is to average many local estimates, each of which is based on a small sketch or batch of the data. Here, we introduce a new technique for debiasing the local estimates, which leads to both theoretical and empirical improvements in the convergence rate of distributed second order methods.
  arXiv  Detail & Related papers  (2020-07-02T18:08:14Z)
• Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model [50.38446482252857]
  This paper is concerned with the sample efficiency of reinforcement learning, assuming access to a generative model (or simulator) We first consider $gamma$-discounted infinite-horizon Markov decision processes (MDPs) with state space $mathcalS$ and action space $mathcalA$. We prove that a plain model-based planning algorithm suffices to achieve minimax-optimal sample complexity given any target accuracy level.
  arXiv  Detail & Related papers  (2020-05-26T17:53:18Z)

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.