Phase estimation with limited coherence

• URL: http://arxiv.org/abs/2207.05656v1
• Date: Tue, 12 Jul 2022 16:36:59 GMT
• Title: Phase estimation with limited coherence
• Authors: D. Munoz-Lahoz, J. Calsamiglia, J. A. Bergou, and E. Bagan
• Abstract summary: For pure states, we give the minimum estimation variance attainable, $V(C)$, and the optimal state, in the limit when the probe system size, $n$, is large. We show that the variance exhibits a Heisenberg-like scaling, $V(C) sim a_n/C2$, where $a_n$ decreases to $pi2/3$ as $n$ increases, leading to a dimension-independent relation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the ultimate precision limits for quantum phase estimation in terms of the coherence, $C$, of the probe. For pure states, we give the minimum estimation variance attainable, $V(C)$, and the optimal state, in the asymptotic limit when the probe system size, $n$, is large. We prove that pure states are optimal only if $C$ scales as $n$ with a sufficiently large proportionality factor, and that the rank of the optimal state increases with decreasing $C$, eventually becoming full-rank. We show that the variance exhibits a Heisenberg-like scaling, $V(C) \sim a_n/C^2$, where $a_n$ decreases to $\pi^2/3$ as $n$ increases, leading to a dimension-independent relation.

Related papers

• Optimal convergence rates in trace distance and relative entropy for the quantum central limit theorem [2.7855886538423182]
  We show that for a centered $m$-mode quantum state with finite third-order moments, the trace distance between $rhoboxplus n$ and $rho_G$ decays at the optimal rate of $mathcalO(n-1/2)$. For states with finite fourth-order moments, we prove that the relative entropy between $rhoboxplus n$ and $rho_G$ decays at the optimal rate of $mathcalO(n-1)$.
  arXiv  Detail & Related papers  (2024-10-29T12:35:47Z)
• Measuring quantum relative entropy with finite-size effect [53.64687146666141]
  We study the estimation of relative entropy $D(rho|sigma)$ when $sigma$ is known. Our estimator attains the Cram'er-Rao type bound when the dimension $d$ is fixed.
  arXiv  Detail & Related papers  (2024-06-25T06:07:20Z)
• Further Understanding of a Local Gaussian Process Approximation: Characterising Convergence in the Finite Regime [1.3518297878940662]
  We show that common choices of kernel functions for a highly accurate and massively scalable GPnn regression model exhibit gradual convergence to behaviour as dataset-size $n$ increases. Similar bounds can be found under model misspecification and combined to give overall rates of convergence of both MSE and an important calibration metric.
  arXiv  Detail & Related papers  (2024-04-09T10:47:01Z)
• Diffusive entanglement growth in a monitored harmonic chain [0.0]
  We find that entanglement grows diffusively ($S sim t1/2$) for a large class of initial Gaussian states. We propose a modified quasi-particle picture which accounts for all of these main features and agrees quantitatively well with our essentially exact numerical results.
  arXiv  Detail & Related papers  (2024-03-06T20:07:25Z)
• Fundamental limits of metrology at thermal equilibrium [0.0]
  We consider the estimation of an unknown parameter $theta$ through a quantum probe at thermal equilibrium. We find the maximal Quantum Fisher Information attainable via arbitrary $HC$, which provides a fundamental bound on the measurement precision.
  arXiv  Detail & Related papers  (2024-02-09T18:01:45Z)
• Localization in 1D non-parametric latent space models from pairwise affinities [6.982738885923206]
  We consider the problem of estimating latent positions in a one-dimensional torus from pairwise affinities. We introduce an estimation procedure that provably localizes all the latent positions with a maximum error of the order of $sqrtlog(n)/n$, with high-probability.
  arXiv  Detail & Related papers  (2021-08-06T13:05:30Z)
• Stochastic Shortest Path: Minimax, Parameter-Free and Towards Horizon-Free Regret [144.6358229217845]
  We study the problem of learning in the shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus. We prove that EB-SSP achieves the minimax regret rate $widetildeO(B_star sqrtS A K)$, where $K$ is the number of episodes, $S$ is the number of states, $A$
  arXiv  Detail & Related papers  (2021-04-22T17:20:48Z)
• Improved Sample Complexity for Incremental Autonomous Exploration in MDPs [132.88757893161699]
  We learn the set of $epsilon$-optimal goal-conditioned policies attaining all states that are incrementally reachable within $L$ steps. DisCo is the first algorithm that can return an $epsilon/c_min$-optimal policy for any cost-sensitive shortest-path problem.
  arXiv  Detail & Related papers  (2020-12-29T14:06:09Z)
• Finding Global Minima via Kernel Approximations [90.42048080064849]
  We consider the global minimization of smooth functions based solely on function evaluations. In this paper, we consider an approach that jointly models the function to approximate and finds a global minimum.
  arXiv  Detail & Related papers  (2020-12-22T12:59:30Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)
• A Simple Convergence Proof of Adam and Adagrad [74.24716715922759]
  We show a proof of convergence between the Adam Adagrad and $O(d(N)/st)$ algorithms. Adam converges with the same convergence $O(d(N)/st)$ when used with the default parameters.
  arXiv  Detail & Related papers  (2020-03-05T01:56:17Z)

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.