Noise-induced decoherence-free zones for anyons

• URL: http://arxiv.org/abs/2510.06094v2
• Date: Mon, 20 Oct 2025 13:14:46 GMT
• Title: Noise-induced decoherence-free zones for anyons
• Authors: Eric R. Bittner,
• Abstract summary: We develop a framework for anyonic systems in which the exchange phase is promoted from a fixed parameter to a fluctuating quantity.<n>We show that the protected mode always minimizes its dephasing at $thetastar = pi/2$, independent of the specific form of $D$.<n>This highlights a simple design rule for optimizing coherence in noisy anyonic systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a stochastic framework for anyonic systems in which the exchange phase is promoted from a fixed parameter to a fluctuating quantity. Starting from the Stratonovich stochastic Liouville equation, we perform the Stratonovich--It\^o conversion to obtain a Lindblad master equation that ties the dissipator directly to the distorted anyon algebra. This construction produces a statistics--dependent dephasing channel, with rates determined by the eigenstructure of the real symmetric correlation matrix $D_{ab}$. The eigenvectors of $D$ select which collective exchange currents -- equivalently, which irreducible representations of the system -- are protected from stochastic dephasing, providing a natural mechanism for decoherence-free subspaces and noise-induced exceptional points. The key result of our analysis is the universality of the optimal statistical angle: in the minimal two-site model with balanced gain and loss, the protected mode always minimizes its dephasing at $\theta^\star = \pi/2$, independent of the specific form of $D$. This robustness highlights a simple design rule for optimizing coherence in noisy anyonic systems, with direct implications for ultracold atomic realizations and other emerging platforms for fractional statistics.

Related papers

• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees [9.180350432640912]
  We study the sampling efficiency of score-based discrete diffusion models under a continuous-time Markov chain (CTMC) formulation.<n>For uniform discrete diffusion, we show that the $$-leaping algorithm achieves an complexity of order $tilde O(d/varepsilon)$.<n>For masking discrete diffusion, we introduce a modified $$-leaping sampler whose convergence rate is governed by an intrinsic information-theoretic quantity.
  arXiv  Detail & Related papers  (2026-02-16T18:48:17Z)
• Decoherence, Perturbations and Symmetry in Lindblad Dynamics [0.0]
  We extend a perturbative Dyson-type treatment and discrete-symmetry constraints from the Schrdinger and von Neumann equations to a dephasing Lindblad framework.<n>This work develops further the odd-symmetric formulation -- based on realism and dual temporal boundary conditions -- from general dynamical considerations to specific tools of quantum mechanics.
  arXiv  Detail & Related papers  (2026-02-14T23:23:29Z)
• Stabilizing Fixed-Point Iteration for Markov Chain Poisson Equations [49.702772230127465]
  We study finite-state Markov chains with $n$ states and transition matrix $P$.<n>We show that all non-decaying modes are captured by a real peripheral invariant subspace $mathcalK(P)$, and that the induced operator on the quotient space $mathbbRn/mathcalK(P) is strictly contractive, yielding a unique quotient solution.
  arXiv  Detail & Related papers  (2026-01-31T02:57:01Z)
• Emergent criticality in a constrained boson model [0.0]
  We show, via explicit computation on a constrained bosonic model, that the presence of subsystem symmetries can lead to a quantum phase transition.<n>We verify this scenario via explicit exact-diagonalization computations, provide an effective Landau-Ginzburg theory for such a transition, and discuss the connection of our model to the PXP model describing Rydberg atom arrays.
  arXiv  Detail & Related papers  (2023-11-20T19:00:03Z)
• From Spectral Theorem to Statistical Independence with Application to System Identification [11.98319841778396]
  We provide first quantitative handle on decay rate of finite powers of state transition matrix $|Ak|$. It is shown that when a stable dynamical system has only one distinct eigenvalue and discrepancy of $n-1$: $|A|$ has a dependence on $n$, resulting dynamics are inseparable. We show that element-wise error is essentially a variant of well-know Littlewood-Offord problem.
  arXiv  Detail & Related papers  (2023-10-16T15:40:43Z)
• A Robustness Analysis of Blind Source Separation [91.3755431537592]
  Blind source separation (BSS) aims to recover an unobserved signal from its mixture $X=f(S)$ under the condition that the transformation $f$ is invertible but unknown. We present a general framework for analysing such violations and quantifying their impact on the blind recovery of $S$ from $X$. We show that a generic BSS-solution in response to general deviations from its defining structural assumptions can be profitably analysed in the form of explicit continuity guarantees.
  arXiv  Detail & Related papers  (2023-03-17T16:30:51Z)
• Globally Convergent Policy Search over Dynamic Filters for Output Estimation [64.90951294952094]
  We introduce the first direct policy search algorithm convex which converges to the globally optimal $textitdynamic$ filter. We show that informativity overcomes the aforementioned degeneracy.
  arXiv  Detail & Related papers  (2022-02-23T18:06:20Z)
• The Schr\"odinger Bridge between Gaussian Measures has a Closed Form [101.79851806388699]
  We focus on the dynamic formulation of OT, also known as the Schr"odinger bridge (SB) problem. In this paper, we provide closed-form expressions for SBs between Gaussian measures.
  arXiv  Detail & Related papers  (2022-02-11T15:59:01Z)
• Hyperspectral Image Denoising Using Non-convex Local Low-rank and Sparse Separation with Spatial-Spectral Total Variation Regularization [49.55649406434796]
  We propose a novel non particular approach to robust principal component analysis for HSI denoising. We develop accurate approximations to both rank and sparse components. Experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method.
  arXiv  Detail & Related papers  (2022-01-08T11:48:46Z)
• Optimal policy evaluation using kernel-based temporal difference methods [78.83926562536791]
  We use kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process. We derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator. We prove minimax lower bounds over sub-classes of MRPs.
  arXiv  Detail & Related papers  (2021-09-24T14:48:20Z)
• Unified Convergence Analysis for Adaptive Optimization with Moving Average Estimator [75.05106948314956]
  We show that an increasing large momentum parameter for the first-order moment is sufficient for adaptive scaling.<n>We also give insights for increasing the momentum in a stagewise manner in accordance with stagewise decreasing step size.
  arXiv  Detail & Related papers  (2021-04-30T08:50:24Z)
• Surveying the Multicomponent Scattering Matrix: Unitarity and Symmetries [0.0]
  We derive a robust theoretical procedure, which is fundamental in quantum-transport problems for unitarity preservation. We predict the interplay for the state-vector transfer matrix, together with the large values of its condition number, as a novel complementary tools for a more accurate definition of the threshold for tunnelling channels.
  arXiv  Detail & Related papers  (2020-10-29T20:37:37Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)
• Tight Nonparametric Convergence Rates for Stochastic Gradient Descent under the Noiseless Linear Model [0.0]
  We analyze the convergence of single-pass, fixed step-size gradient descent on the least-square risk under this model. As a special case, we analyze an online algorithm for estimating a real function on the unit interval from the noiseless observation of its value at randomly sampled points.
  arXiv  Detail & Related papers  (2020-06-15T08:25:50Z)
• A Precise High-Dimensional Asymptotic Theory for Boosting and Minimum-$\ell_1$-Norm Interpolated Classifiers [3.167685495996986]
  This paper establishes a precise high-dimensional theory for boosting on separable data. Under a class of statistical models, we provide an exact analysis of the universality error of boosting. We also explicitly pin down the relation between the boosting test error and the optimal Bayes error.
  arXiv  Detail & Related papers  (2020-02-05T00:24:53Z)

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.