Central Limit Theorems for Outcome Records in Disordered Quantum Trajectories

• URL: http://arxiv.org/abs/2603.28893v1
• Date: Mon, 30 Mar 2026 18:17:02 GMT
• Title: Central Limit Theorems for Outcome Records in Disordered Quantum Trajectories
• Abstract summary: We prove CLT for finite pattern counts in the measurement record of discrete-time quantum trajectories generated by repeated measurements in a disordered environment.<n>We provide criteria and verify the assumptions across a broad family of examples, including disordered walk-type models generated by finite group actions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove annealed central limit theorems for finite pattern counts in the measurement record of discrete-time quantum trajectories generated by repeated measurements in a disordered environment. Under summable mixing assumptions on the environment and an annealed trace-norm forgetting property for the associated non-selective channel cocycle, we first establish the CLT under the annealed law determined by the dynamically stationary state. This part applies to general disordered quantum instruments and, in particular, is not restricted to the perfect-measurement regime; it complements both the corresponding law of large numbers for disordered measurement records and the homogeneous central limit theorem. We then introduce a coupling-based notion of admissibility for initial states and show that the same Gaussian limit extends to every admissible initial law, with unchanged centering and asymptotic variance. In the perfect-measurement setting, we further identify a general condition ensuring admissibility for every initial state, and hence obtain a universal annealed central limit theorem. We also provide practical sufficient criteria for this condition and verify the assumptions across a broad family of examples, including disordered walk-type models generated by finite group actions

Related papers

• Boltzmann counting in Hilbert space [39.146761527401424]
  We introduce a geometric entropy for quantum preparations, defined as the logarithm of the Hilbert-space volume of pure states compatible with a given set of constraints.<n>We analyze three classes of constraints: restriction to a subspace, fixed expectation values, and coarse-grained subsystem descriptions.<n>The resulting framework provides a geometric measure of quantum ignorance at the level of the preparation.
  arXiv  Detail & Related papers  (2026-08-20T15:01:51Z)
• Relational Quantum Causal Processes: Exact Models, Continuum Limits, and the Boundary of Emergent Gravity [0.875682288556859]
  We present a framework that separates established mechanisms, conditional compositions, and open assumptions.<n>CP-QG as a microscopic-indexed framework that separates established mechanisms, conditional compositions, and open assumptions.
  arXiv  Detail & Related papers  (2026-07-29T09:28:18Z)
• Quantum Metric Bound State of Light [0.2624902795082451]
  We prove that the exponential decay length of defect-induced bound states is lower-bounded by the quantum metric of the unperturbed flat band.<n>This is a predictive design principle for engineering confined modes in synthetic wave platforms.
  arXiv  Detail & Related papers  (2026-06-21T12:40:53Z)
• Sub-Gaussian Concentration and Entropic Normality of the Maximum Likelihood Estimator [14.681656119120584]
  It is well known that, under standard regularity conditions, the maximum likelihood estimator satisfies a central limit theorem.<n>This paper develops several stronger forms of normality for the normalized MLE.<n> auxiliary tools that may be of independent interest, including exponential consistency bounds, high-moment estimates, and entropy-control arguments for the estimator.
  arXiv  Detail & Related papers  (2026-05-08T01:34:03Z)
• Typical entanglement in anyon chains: Page curves beyond Lie group symmetries [41.99844472131922]
  We study bipartite entanglement statistics in one-dimensional anyon chains constrained by fusion rules of unitary pre-modular categories.<n>Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(sqrtL)$ or $O(1)$ symmetry-type corrections.<n> Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions.
  arXiv  Detail & Related papers  (2026-03-26T18:00:03Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• A Necessary and Sufficient Condition for Quantum Realizability of Correlations for Arbitrary Normalized Observables in the Clauser--Horne--Shimony--Holt Setup [0.8024120666398408]
  We establish a quantum state that reproduces given correlation values in the Clauser--Horne--Shimony--Holt setup for any fixed normalized observables.<n>We show that our condition applies to Bell's original scenario and reveals that whether Bell's original inequality is violated depends sensitively on the chosen observables.
  arXiv  Detail & Related papers  (2025-03-07T15:45:56Z)
• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation [39.20075231137991]
  We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems.<n> scaling these methods to larger system sizes reveals three key challenges: the smoothness of the CDF for large supports, the lack of tight lower bounds on the overlap with the true ground state, and the difficulty of preparing high-quality initial states.
  arXiv  Detail & Related papers  (2024-05-06T18:00:03Z)
• A note on typicality in random quantum scattering [0.0]
  We consider scattering processes where a quantum system is comprised of an inner subsystem and of a boundary. We show that, regardless of the initial state, a single scattering event will disentangle the unconditional state across the inner subsystem-boundary partition.
  arXiv  Detail & Related papers  (2023-08-29T17:42:25Z)
• A Measure-Theoretic Axiomatisation of Causality [55.6970314129444]
  We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
  arXiv  Detail & Related papers  (2023-05-19T13:15:48Z)
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition [62.997667081978825]
  We analyze the role of boundary conditions in the statistics of topological defects. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
  arXiv  Detail & Related papers  (2022-07-08T09:55:05Z)
• Measurement disturbance and conservation laws in quantum mechanics [0.0]
  We provide novel quantitative bounds demonstrating necessary conditions under which accurate or non-disturbing measurements can be achieved. We obtain a substantial generalisation of the Wigner-Araki-Yanase (WAY) theorem.
  arXiv  Detail & Related papers  (2021-10-22T11:03:23Z)
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States [0.0]
  We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems. Under a condition of Local Topological Quantum Order, the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential.
  arXiv  Detail & Related papers  (2020-10-29T03:24:19Z)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)
• Generalized Sliced Distances for Probability Distributions [47.543990188697734]
  We introduce a broad family of probability metrics, coined as Generalized Sliced Probability Metrics (GSPMs) GSPMs are rooted in the generalized Radon transform and come with a unique geometric interpretation. We consider GSPM-based gradient flows for generative modeling applications and show that under mild assumptions, the gradient flow converges to the global optimum.
  arXiv  Detail & Related papers  (2020-02-28T04:18:00Z)

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.