The Decoherence Exponent: Stable Phase Noise and Constraints on Objective State Reduction

• URL: http://arxiv.org/abs/2608.18335v1
• Date: Tue, 18 Aug 2026 21:36:16 GMT
• Title: The Decoherence Exponent: Stable Phase Noise and Constraints on Objective State Reduction
• Abstract summary: Averaging $eiL_uQ$ gives a completely positive dephasing semigroup.<n>Schoenberg's theorem ensures complete positivity for any finite real spectrum when $0le2$.<n>For a bounded reduction walk, we prove Born probabilities for every symmetric bounded proposal law.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Let $L_u$ be a symmetric Levy process representing an unobserved phase lift, coupling to a quantum system via charge $Q$. Averaging $e^{iL_uQ}$ gives a completely positive dephasing semigroup. If the characteristic exponent lacks an intrinsic charge scale, the Levy-Khintchine theorem forces $η(ξ)=D | ξ|^α$ ($0<α\le2$), so coherences decay at $Γ_{ab}=D | q_a-q_b |^α$. For integer charge differences, the process descends to the wrapped variable $Θ_u=L_u\bmod 2π$; for real charges, the lift is the relevant phase. Schoenberg's theorem ensures complete positivity for any finite real spectrum when $0<α\le2$, while $α>2$ yields an analytic obstruction. This boundary is exact, verified numerically here. A Gaussian integrated phase gives quadratic charge dependence, though colored Gaussian noise need not yield a Markov semigroup. Two idealized non-Gaussian mechanisms are analyzed: inverse-power Poisson shot noise ($α=d/p$) and Bochner subordination of Brownian phase by an $α/2$-stable clock. For a bounded reduction walk, we prove Born probabilities for every symmetric bounded proposal law. Simulations of truncated stable laws ($α=0.5,1,1.5,2$) confirm this law-independence. In continuous time, $α$-stable drivers fail to reduce: the exact-flow (Marcus) equation oscillates, and the naive Ito jump equation fails to preserve state. For Gaussian white noise, the Itô model collapses to Born probabilities, whereas the exact-flow (Stratonovich) model does not collapse without a threshold and yields non-Born exit probabilities. The quadratic case recovers Milburn's small-step limit, not his exact Poisson dynamics. Finally, a bi-temporal geometry is examined as a possible compact phase source, but closed timelike curves, nonunitary evolution, and an unstable mode tower prevent a consistent field-theoretic realization.

Related papers

• Constrained Online Learning with Noisy Constraint Values [55.29259818039367]
  Under common feasibility, our LEDGER algorithm attains $O(sqrt T)$ expected regret and $O(sqrtTlog(eT))$ expected budget violation.<n>Neither a Slater condition, independence between feedback channels, nor an absolute constraint-value bound is needed.
  arXiv  Detail & Related papers  (2026-09-07T01:38:41Z)
• Restricted Eigenvalues Beyond Gaussian Width: Threshold Occupancy under Heavy Tails [47.36630149538994]
  For isotropic sub-Gaussian measurements, the benchmark sample size is $1+w(A)2$, where $w(A)$ is the Gaussian width of the normalized descent cone.<n>We give an explicit and systematic negative answer to the general question as formulated there: the proposed law fails in its full dimension-free, arbitrary-set form.<n>Under isotropy, a distribution-free fallback governed by affine dimension times squared enclosing radius is sharp on this family.
  arXiv  Detail & Related papers  (2026-09-03T08:05:05Z)
• The Physical Cutoff Does Not Restore Homogenization: Phase-Dependent Burning in the Strain G-Equation [2.538209532048867]
  We prove that for any $C2$ incompressible periodic flow, every $varepsilon$-outward barrier certificate has covering radius at most $2dvarepsilon$ for all sufficiently small $varepsilon$.
  arXiv  Detail & Related papers  (2026-08-15T17:41:14Z)
• Teleportation through time-varying channels: threshold geometry and a complete-positivity bound on non-Markovian backflow [0.0]
  A Bell pair distributed through a link has dynamics that separate into a fixed part and a moving one.<n>The negativity, fully entangled fraction, discord, and average teleportation fidelity depend on time only through the accumulated damping parameters.
  arXiv  Detail & Related papers  (2026-08-11T18:03:16Z)
• Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise [49.730496294398726]
  We develop a novel quantum mean estimator for heavy-tailed random variables.<n>We derive stronger lower bounds for tail index>4/3$, showing that a nontrivial dependence on a dimension is unavoidable.<n>For a convex objective function, we propose a quantum projected gradient descent method.
  arXiv  Detail & Related papers  (2026-07-28T09:29:37Z)
• An Optimal Analysis of the Product Test [42.29010058743949]
  Product testing decides whether a pure multipartite quantum state is fully unentangled across a specified tensor decomposition.<n>Despite being a fundamental property testing task and having many applications, the product test's exact (worst-case) acceptance probability curve has yet to be fully determined.<n>As a complexity-theoretic application, our results improve the one-shot soundness parameter in the Harrow-Montanaro reduction from $mathsfQMA(k)$ to $mathsfQMA(2)$.
  arXiv  Detail & Related papers  (2026-07-23T16:17:44Z)
• Fixed-Boost Wigner Noise: Strict Trace-Distance Contraction without Quantum Degradability [0.0]
  A Lorentz boost acts on the canonical spin of a massive particle through a momentum-dependent Wigner rotation.<n>We show that, for one fixed observer boost, reducing over an uncertain momentum can strictly contract every pairwise spin-state trace distance.
  arXiv  Detail & Related papers  (2026-07-14T17:46:52Z)
• Finite-Sample Performance of Gradient Descent in Logistic Regression with Gaussian Design [28.74829605004241]
  We characterize the finite-sample estimation performance and convergence behavior of gradient descent (GD) on the maximum likelihood objective (i.e., the logistic loss)<n>We show that GD linearly converges to a small neighborhood of $*$ achieving an $ell$ error of order $O(sqrt|*|5d/n)$.<n>We also establish a faster local linear convergence to the same statistical error under a large $(|*|_2)$ stepsize.
  arXiv  Detail & Related papers  (2026-06-19T18:43:41Z)
• Nonlinear Two-Time-Scale Stochastic Approximation: A Sharp Phase Transition and How to Beat It [46.80389197344682]
  We prove localized transfer theorems that extend the phase-transition mechanism to general nonlinear TTSA.<n>The proofs are non-asymptotic and rely on two Abel-transform cancellations.
  arXiv  Detail & Related papers  (2026-06-12T14:24:28Z)
• Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability [0.0]
  We identify the wavelet scaling exponent $$ as a critical diagnostic.<n>We establish $= 1/2$ as a sharp transition boundary for the classical simulability of amplitude-encoded quantum kernels.<n>We prove this variance scales strictly as $Var[X] = (d-2)$.
  arXiv  Detail & Related papers  (2026-05-12T05:41:12Z)
• When Does $\ell_2$-Boosting Overfit Benignly? High-Dimensional Risk Asymptotics and the $\ell_1$ Implicit Bias [15.113649527486276]
  We show that benign overfitting fails at the linear rate.<n>We show that while this localization mechanism should persist in the presence of signals, the exact signal-noise decomposition remains an open problem.
  arXiv  Detail & Related papers  (2026-05-07T14:14:09Z)
• Quantum Brownian motion with non-Gaussian noises: Fluctuation-Dissipation Relation and nonlinear Langevin equation [0.0]
  We consider the quantum Brownian motion (QBM) model with one oscillator as the system.<n>The influence action $S_IF$ is calculated using a perturbative expansion in $$.<n>The non-Gaussian noise kernel gives rise to non-zero three-point correlation function of the corresponding force.
  arXiv  Detail & Related papers  (2026-02-11T02:03:26Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• On quantum algorithms for the Schr\"odinger equation in the semi-classical regime [27.175719898694073]
  We consider Schr"odinger's equation in the semi-classical regime. Such a Schr"odinger equation finds many applications, including in Born-Oppenheimer molecular dynamics and Ehrenfest dynamics.
  arXiv  Detail & Related papers  (2021-12-25T20:01:54Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)

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.