Observable Statistical Mechanics

• URL: http://arxiv.org/abs/2309.15173v3
• Date: Tue, 29 Jul 2025 17:28:32 GMT
• Title: Observable Statistical Mechanics
• Authors: Lodovico Scarpa, Abdulla Alhajri, Vlatko Vedral, Fabio Anza,
• Abstract summary: We propose a general and computationally easy approach to determine the stationary probability distribution of observables.<n>We show that the resulting theory accurately predicts stationary probability distributions without detailed microscopic information like the energy eigenstates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many scenarios where this is not possible and one must instead use another ensemble, such as the diagonal, microcanonical or generalized Gibbs ensembles. However, these all require detailed information about the energy or other conserved quantities to be constructed. Here we propose a general and computationally easy approach to determine the stationary probability distribution of observables with few outcomes. Interpreting coarse measurements at equilibrium as noisy communication channels, we provide general analytical arguments in favor of the applicability of a maximum entropy principle for this class of observables. We show that the resulting theory accurately predicts stationary probability distributions without detailed microscopic information like the energy eigenstates. Extensive numerical experiments on 7 non-weakly interacting spin-1/2 Hamiltonians demonstrate the broad applicability and robustness of this framework in both quantum integrable and chaotic models.

Related papers

• Work Statistics and Quantum Trajectories: No-Click Limit and non-Hermitian Hamiltonians [50.24983453990065]
  We present a framework for quantum work statistics in continuously monitored quantum systems. Our approach naturally incorporates non-Hermitian dynamics arising from quantum jump processes. We illustrate our theoretical framework by analyzing a one-dimensional transverse-field Ising model under local spin monitoring.
  arXiv  Detail & Related papers  (2025-04-15T23:21:58Z)
• Universal Hamming Weight Preserving Variational Quantum Ansatz [48.982717105024385]
  Understanding variational quantum ans"atze is crucial for determining quantum advantage in Variational Quantum Eigensolvers (VQEs) This work highlights the critical role of symmetry-preserving ans"atze in VQE research, offering insights that extend beyond supremacy debates.
  arXiv  Detail & Related papers  (2024-12-06T07:42:20Z)
• Compatibility of Quantum Measurements and the Emergence of Classical Objectivity [0.0]
  We consider the KDQ distributions describing arbitrary collections of measurements on disjoint components of some generic multipartite system. We show that the system dynamics ensures that these distributions are classical if and only if the Hamiltonian supports Quantum Darwinism.
  arXiv  Detail & Related papers  (2024-11-16T19:01:30Z)
• One-Shot Min-Entropy Calculation Of Classical-Quantum States And Its Application To Quantum Cryptography [21.823963925581868]
  We develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state.<n>It offers an alternative tight finite-data analysis for the BB84 quantum key distribution scheme.<n>It gives the best finite-key bound known to date for a variant of device independent quantum key distribution protocol.
  arXiv  Detail & Related papers  (2024-06-21T15:11:26Z)
• Out-of-equilibrium Eigenstate Thermalization Hypothesis [0.0]
  Understanding how out-of-equilibrium states thermalize under quantum unitary dynamics is an important problem in many-body physics. We propose a statistical ansatz for the matrix elements of non-equilibrium initial states in the energy eigenbasis. We numerically verify scaling and cross-correlation, point out the emergent universality of the high-frequency behavior, and outline possible generalizations.
  arXiv  Detail & Related papers  (2024-06-07T06:54:14Z)
• Evolution of expected values in open quantum systems [41.94295877935867]
  We show that in some cases the power performed by the system can be considered as a quantum observable.<n>As an application, the pure dephasing process is reinterpreted from this perspective.
  arXiv  Detail & Related papers  (2024-02-29T06:47:28Z)
• Universality in driven open quantum matter [0.0]
  Universality is a powerful concept, which enables making qualitative and quantitative predictions in systems with extensively many degrees of freedom. We focus here on its manifestations within a specific class of nonequilibrium stationary states: driven open quantum matter.
  arXiv  Detail & Related papers  (2023-12-05T19:00:07Z)
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling [49.1574468325115]
  A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single- parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics. We establish that scaling predictions are matched by a privileged process, and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all timescales.
  arXiv  Detail & Related papers  (2023-10-17T15:41:50Z)
• Continuously Monitored Quantum Systems beyond Lindblad Dynamics [68.8204255655161]
  We study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state.
  arXiv  Detail & Related papers  (2023-05-06T18:09:17Z)
• Indeterminate Probability Theory [18.320645632562663]
  This paper proposes Indeterminate Probability Theory (IPT)<n>IPT is an observer-centered framework in which experimental outcomes are represented as distributions combining ground truth with observation error.<n>IPT is consistent with classical probability theory and subsumes the frequentist equation in the limit of vanishing observation error.
  arXiv  Detail & Related papers  (2023-03-21T01:57:40Z)
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain [62.997667081978825]
  We show that local projective measurements induce a modification of the out-of-equilibrium probability distribution function of the local magnetization. In particular we describe how the probability distribution of the former shows different behaviour in the area-law and volume-law regimes.
  arXiv  Detail & Related papers  (2022-12-19T12:34:37Z)
• Quantum Mechanics: Statistical Balance Prompts Caution in Assessing Conceptual Implications [0.0]
  Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical states, and not yet explained. "statistical balance" now refers to a feature of contexts in which there is a prescribed probability other than 0 or 1. Unexplained statistical balance prompts caution in assessing the conceptual implications of entanglement, measurement, uncertainty, and two-slit and Bell-type analyses.
  arXiv  Detail & Related papers  (2022-10-27T18:21:38Z)
• Maximum entropy quantum state distributions [58.720142291102135]
  We go beyond traditional thermodynamics and condition on the full distribution of the conserved quantities. The result are quantum state distributions whose deviations from thermal states' get more pronounced in the limit of wide input distributions.
  arXiv  Detail & Related papers  (2022-03-23T17:42:34Z)
• Distinct universality classes of diffusive transport from full counting statistics [0.4014524824655105]
  We study the full counting statistics of spin transport in various integrable and non-integrable anisotropic one-dimensional spin models. We find that spin transport, while diffusive on average, is governed by a distinct non-Gaussian universality class. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays.
  arXiv  Detail & Related papers  (2022-03-17T18:00:01Z)
• Relaxation of non-integrable systems and correlation functions [0.0]
  We investigate early-time equilibration rates of observables in closed many-body quantum systems. We find evidence for this coincidence when the initial conditions are sufficiently generic, or typical. Our findings are confirmed by proving that these different timescales coincide for dynamics generated by Haar-random Hamiltonians.
  arXiv  Detail & Related papers  (2021-12-17T12:34:34Z)
• Quantum thermodynamics under continuous monitoring: a general framework [0.0]
  We provide an introduction to the general theoretical framework to establish and interpret thermodynamics for quantum systems. Main quantities such as work, heat, and entropy production can be defined at the level of thermodynamics. The connection to irreversibility and fluctuation theorems is also discussed, together with some recent developments.
  arXiv  Detail & Related papers  (2021-12-03T17:02:53Z)
• Relaxation of Multitime Statistics in Quantum Systems [0.0]
  We show that most multitime observables for sufficiently large times cannot distinguish a nonequilibrium process from an equilibrium one. A corollary of our results is that the size of non-Markovianity and other multitime characteristics of a nonequilibrium process also equilibrate.
  arXiv  Detail & Related papers  (2021-08-17T03:15:07Z)
• Entanglement Measures in a Nonequilibrium Steady State: Exact Results in One Dimension [0.0]
  Entanglement plays a prominent role in the study of condensed matter many-body systems. We show that the scaling of entanglement with the length of a subsystem is highly unusual, containing both a volume-law linear term and a logarithmic term.
  arXiv  Detail & Related papers  (2021-05-03T10:35:09Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks [48.7576911714538]
  Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
  arXiv  Detail & Related papers  (2020-12-11T12:55:17Z)
• Theory of Ergodic Quantum Processes [0.0]
  We consider general ergodic sequences of quantum channels with arbitrary correlations and non-negligible decoherence. We compute the entanglement spectrum across any cut, by which the bipartite entanglement entropy can be computed exactly. Other physical implications of our results are that most Floquet phases of matter are metastable and that noisy random circuits in the large depth limit will be trivial as far as their quantum entanglement is concerned.
  arXiv  Detail & Related papers  (2020-04-29T18:00:03Z)
• In and out of equilibrium quantum metrology with mean-field quantum criticality [68.8204255655161]
  We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level.
  arXiv  Detail & Related papers  (2020-01-09T19:20:42Z)

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.