Tight bounds on recurrence time in closed quantum systems

• URL: http://arxiv.org/abs/2601.10409v1
• Date: Thu, 15 Jan 2026 14:01:34 GMT
• Title: Tight bounds on recurrence time in closed quantum systems
• Authors: Marcin Kotowski, Michał Oszmaniec,
• Abstract summary: We establish upper bounds on the recurrence time for a pure state evolving under a Hamiltonian $H$.<n>We show that our upper bound on $t_mathrmrec$ is generically saturated for random Hamiltonians.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The evolution of an isolated quantum system inevitably exhibits recurrence: the state returns to the vicinity of its initial condition after finite time. Despite its fundamental nature, a rigorous quantitative understanding of recurrence has been lacking. We establish upper bounds on the recurrence time, $t_{\mathrm{rec}} \lesssim t_{\mathrm{exit}}(ε)(1/ε)^d$, where $d$ is the Hilbert-space dimension, $ε$ the neighborhood size, and $t_{\mathrm{exit}}(ε)$ the escape time from this neighborhood. For pure states evolving under a Hamiltonian $H$, estimating $t_{\mathrm{exit}}$ is equivalent to an inverse quantum speed limit problem: finding upper bounds on the time a time-evolved state $ψ_t$ needs to depart from the $ε$-vicinity of the initial state $ψ_0$. We provide a partial solution, showing that under mild assumptions $t_{\mathrm{exit}}(ε) \approx ε/\sqrt{ Δ(H^2)}$, with $Δ(H^2)$ the Hamiltonian variance in $ψ_0$. We show that our upper bound on $t_{\mathrm{rec}}$ is generically saturated for random Hamiltonians. Finally, we analyze the impact of coherence of the initial state in the eigenbasis of $H$ on recurrence behavior.

Related papers

• Fine-Grained Complexity for Quantum Problems from Size-Preserving Circuit-to-Hamiltonian Constructions [1.43494686131174]
  We show that the 3-local Hamiltonian problem on $n$ qubits cannot be solved classically in time $O(2(1-varepsilon)n)$ for any $varepsilon>0$ under the Strong Exponential-Time Hypothesis (SETH)<n>We provide a quantum algorithm that runs in $O(sqrt2n)$ time for an arbitrary $1/mathrmpoly(n)$ relative error, matching our lower bounds and improving the state-of-the-art algorithm by Bravyi, Chowdhury, Goss
  arXiv  Detail & Related papers  (2026-02-16T01:11:55Z)
• The generalized adiabatic theorem for extended lattice systems [0.9558392439655014]
  We prove an adiabatic theorem for infinitely extended lattice fermion systems with gapped ground states, allowing perturbations that may close the gap.<n>The result provides a rigorous basis for linear response to macroscopic changes in gapped systems, including a proof of Ohm's law for Hall currents.
  arXiv  Detail & Related papers  (2025-10-23T18:10:40Z)
• Approximating the operator norm of local Hamiltonians via few quantum states [53.16156504455106]
  Consider a Hermitian operator $A$ acting on a complex Hilbert space of $2n$.<n>We show that when $A$ has small degree in the Pauli expansion, or in other words, $A$ is a local $n$-qubit Hamiltonian.<n>We show that whenever $A$ is $d$-local, textiti.e., $deg(A)le d$, we have the following discretization-type inequality.
  arXiv  Detail & Related papers  (2025-09-15T14:26:11Z)
• Spectral Gaps with Quantum Counting Queries and Oblivious State Preparation [47.600794349481966]
  In this work, we present a quantum algorithm which approximates values up to additive error $epsilonDelta_k$ using a logarithmic number of qubits.<n>A key technical step in the analysis is the preparation of a suitable random initial state, which ultimately allows us to efficiently count the number of eigenvalues that are smaller than a threshold.
  arXiv  Detail & Related papers  (2025-08-28T17:04:18Z)
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models [0.0]
  We study the out-of-equilibrium dynamics of one-dimensional quantum Ising models in a transverse field $g$.<n>We consider nearest-neighbor Ising chains of size $L$ with periodic boundary conditions.
  arXiv  Detail & Related papers  (2025-04-14T20:00:27Z)
• Semicontinuity bounds for the von Neumann entropy and partial majorization [0.0]
  We consider families of tight upper bounds on the difference $S(rho)-S(sigma)$ with the rank/energy constraint imposed on the state $rho$.<n>The upper bounds within these families depend on the parameter $m$ of partial majorization.
  arXiv  Detail & Related papers  (2025-04-10T19:55:06Z)
• 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 $mathcalO(n-1/2)$.<n>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.<n>Our estimator attains the Cram'er-Rao type bound when the dimension $d$ is fixed.
  arXiv  Detail & Related papers  (2024-06-25T06:07:20Z)
• Stochastic behavior of outcome of Schur-Weyl duality measurement [45.41082277680607]
  We focus on the measurement defined by the decomposition based on Schur-Weyl duality on $n$ qubits. We derive various types of distribution including a kind of central limit when $n$ goes to infinity.
  arXiv  Detail & Related papers  (2021-04-26T15:03:08Z)
• Scattering data and bound states of a squeezed double-layer structure [77.34726150561087]
  A structure composed of two parallel homogeneous layers is studied in the limit as their widths $l_j$ and $l_j$, and the distance between them $r$ shrinks to zero simultaneously. The existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac's delta function. The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.
  arXiv  Detail & Related papers  (2020-11-23T14:40:27Z)
• An Optimal Separation of Randomized and Quantum Query Complexity [67.19751155411075]
  We prove that for every decision tree, the absolute values of the Fourier coefficients of a given order $ellsqrtbinomdell (1+log n)ell-1,$ sum to at most $cellsqrtbinomdell (1+log n)ell-1,$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant.
  arXiv  Detail & Related papers  (2020-08-24T06:50:57Z)
• Entanglement of truncated quantum states [0.0]
  We investigate the impact of Hilbert-space truncation upon the entanglement of an initially maximally entangled $mtimes m$ bipartite quantum state. For a random local unitary evolution, we obtain a simple analytical formula that expresses the truncation-induced entanglement loss as a function of $n$, $m$ and $s$.
  arXiv  Detail & Related papers  (2020-03-16T11:40:18Z)

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.