Volume-law entanglement entropy of typical pure quantum states

• URL: http://arxiv.org/abs/2112.06959v2
• Date: Wed, 27 Jul 2022 03:30:21 GMT
• Title: Volume-law entanglement entropy of typical pure quantum states
• Authors: Eugenio Bianchi, Lucas Hackl, Mario Kieburg, Marcos Rigol, Lev Vidmar
• Abstract summary: In quantum chaotic systems it has been found to behave as in typical pure states. In integrable systems it has been found to behave as in typical pure Gaussian states.
• Score: 0.8399688944263842
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians has been recently conjectured to be a diagnostic of quantum chaos and integrability. In quantum chaotic systems it has been found to behave as in typical pure states, while in integrable systems it has been found to behave as in typical pure Gaussian states. In this tutorial, we provide a pedagogical introduction to known results about the entanglement entropy of subsystems of typical pure states and of typical pure Gaussian states. They both exhibit a leading term that scales with the volume of the subsystem, when smaller than one half of the volume of the system, but the prefactor of the volume law is fundamentally different. It is constant (and maximal) for typical pure states, and it depends on the ratio between the volume of the subsystem and of the entire system for typical pure Gaussian states. Since particle-number conservation plays an important role in many physical Hamiltonians, we discuss its effect on typical pure states and on typical pure Gaussian states. We prove that while the behavior of the leading volume-law terms does not change qualitatively, the nature of the subleading terms can change. In particular, subleading corrections can appear that depend on the square root of the volume of the subsystem. We unveil the origin of those corrections. Finally, we discuss the connection between the entanglement entropy of typical pure states and analytical results obtained in the context of random matrix theory, as well as numerical results obtained for physical Hamiltonians.

Related papers

• Information upper bounds in composite quantum systems [11.005712568346414]
  We decompose the quantum state and focus on the total amount of information contained in the components that constitute the legal quantum state itself. We analytically proved that the upper bound of the posterior information content of quantum pure states is exactly equal to 2.
  arXiv  Detail & Related papers  (2024-11-14T03:00:29Z)
• Deep thermalization in continuous-variable quantum systems [2.979579757819132]
  We study the ensemble of pure states supported on a small subsystem of a few modes. We find that the induced ensemble attains a universal form, independent of the choice of measurement basis.
  arXiv  Detail & Related papers  (2024-05-09T00:01:23Z)
• Exploring Hilbert-Space Fragmentation on a Superconducting Processor [23.39066473461786]
  Isolated interacting quantum systems generally thermalize, yet there are several counterexamples for the breakdown of ergodicity. Recently, ergodicity breaking has been observed in systems subjected to linear potentials, termed Stark many-body localization. Here, we experimentally explore initial-state dependent dynamics using a ladder-type superconducting processor with up to 24 qubits.
  arXiv  Detail & Related papers  (2024-03-14T04:39:14Z)
• Canonical typicality under general quantum channels [39.58317527488534]
  In the present work we employ quantum channels to define generalized subsystems. We show that generalized subsystems also display the phenomena of canonical typicality. In particular we demonstrate that the property regulating the emergence of the canonical typicality behavior is the entropy of the channel used to define the generalized subsystem.
  arXiv  Detail & Related papers  (2023-08-30T21:29:45Z)
• Polaritonic Ultrastrong Coupling: Quantum Entanglement in Ground State [0.0]
  We study the ultrastrong coupling between the elementary excitations of matter and microcavity modes. The amount of quantum entanglement in the ground state is quite significant in the ultrastrong coupling regime.
  arXiv  Detail & Related papers  (2023-04-03T01:58:23Z)
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States [15.208790082352351]
  distillable randomness of a bipartite quantum state is an information-theoretic quantity. We prove measures of classical correlations and prove a number of their properties. We then further bound these measures from above by some that are efficiently computable by means of semi-definite programming.
  arXiv  Detail & Related papers  (2022-12-18T12:06:25Z)
• Universal equilibration dynamics of the Sachdev-Ye-Kitaev model [11.353329565587574]
  We present a universal feature in the equilibration dynamics of the Sachdev-Ye-Kitaev (SYK) Hamiltonian. We reveal that the disorder-averaged evolution of few-body observables, including the quantum Fisher information, exhibit within numerical resolution a universal equilibration process. This framework extracts the disorder-averaged dynamics of a many-body system as an effective dissipative evolution.
  arXiv  Detail & Related papers  (2021-08-03T19:43:58Z)
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states [11.04121146441257]
  We prove that the entanglement entropy of any pure initial state of a bosonic quantum system grows linearly in time. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems.
  arXiv  Detail & Related papers  (2021-07-23T07:55:38Z)
• 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)
• Extremal quantum states [0.41998444721319206]
  We peruse quantumness from a variety of viewpoints, concentrating on phase-space formulations. The symmetry-transcending properties of the Husimi $Q$ function make it our basic tool. We use these quantities to formulate extremal principles and determine in this way which states are the most and least "quantum"
  arXiv  Detail & Related papers  (2020-10-09T18:00:02Z)

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.