Entanglement of Local Operators and the Butterfly Effect

• URL: http://arxiv.org/abs/2005.14243v2
• Date: Mon, 1 Feb 2021 17:29:26 GMT
• Title: Entanglement of Local Operators and the Butterfly Effect
• Authors: Jonah Kudler-Flam, Masahiro Nozaki, Shinsei Ryu, Mao Tian Tan
• Abstract summary: We study the robustness of quantum and classical information to perturbations implemented by local operator insertions. We do this by computing multipartite entanglement measures in the Hilbert space of local operators in the Heisenberg picture.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the robustness of quantum and classical information to perturbations implemented by local operator insertions. We do this by computing multipartite entanglement measures in the Hilbert space of local operators in the Heisenberg picture. The sensitivity to initial conditions that we explore is an illuminating manifestation of the butterfly effect in quantum many-body systems. We derive a "membrane theory" in Haar random unitary circuits to compute the mutual information, logarithmic negativity, and reflected entropy in the local operator state by mapping to a classical statistical mechanics problem and find that any local operator insertion delocalizes information as fast as is allowed by causality. Identical behavior is found for conformal field theories admitting holographic duals where the bulk geometry is described by the eternal black hole with a local object situated at the horizon. In contrast to these maximal scramblers, only an $O(1)$ amount of information is found to be delocalized by local operators in integrable systems such as free fermions and Clifford circuits.

Related papers

• Engineering Transport via Collisional Noise: a Toolbox for Biology Systems [44.99833362998488]
  We study a generalised XXZ model in the presence of collision noise, which allows to describe environments beyond the standard Markovian formulation. Results constitute an example of the essential building blocks for the understanding of quantum transport in noisy and warm disordered environments.
  arXiv  Detail & Related papers  (2023-11-15T12:55:28Z)
• Identification of a natural fieldlike entanglement resource in trapped-ion chains [0.0]
  The electromagnetic trapping of ion chains can be regarded as a process of non-trivial entangled quantum state preparation. The decay of entanglement between disjoint subsets of local modes is found to exhibit features of entanglement structure. A framework is established for initializing quantum field simulations via "imaging" extended entangled states from natural sources.
  arXiv  Detail & Related papers  (2023-11-15T10:32:02Z)
• Overlapping qubits from non-isometric maps and de Sitter tensor networks [41.94295877935867]
  We show that processes in local effective theories can be spoofed with a quantum system with fewer degrees of freedom. We highlight how approximate overlapping qubits are conceptually connected to Hilbert space dimension verification, degree-of-freedom counting in black holes and holography.
  arXiv  Detail & Related papers  (2023-04-05T18:08:30Z)
• Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
  Signatures of localization have been observed in condensed matter and cold atomic systems. We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths. We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
  arXiv  Detail & Related papers  (2023-03-13T12:45:25Z)
• Nature and origin of the operators entering the master equation of an open quantum system [0.0]
  We derive an equation of motion for the reduced density operator of an open quantum system. We find Lindblad-like operators for two different models of a qubit in a bosonic environment.
  arXiv  Detail & Related papers  (2022-09-28T16:33:08Z)
• From locality to irregularity: Introducing local quenches in massive scalar field theory [68.8204255655161]
  We consider the dynamics of excited local states in massive scalar field theory in an arbitrary spacetime dimension. We identify different regimes of their evolution depending on the values of the field mass and the quench regularization parameter. We also investigate the local quenches in massive scalar field theory on a cylinder and show that they cause an erratic and chaotic-like evolution of observables.
  arXiv  Detail & Related papers  (2022-05-24T18:00:07Z)
• Local Quantum Theory with Fluids in Space-Time [0.0]
  An explicit, unambiguous, and Lorentz-covariant 'local hidden variable theory' in space-time is presented. There is no inconsistency with Bell's theorem because this a local many-worlds theory. The experience of collapse, Born rule probability, and environmental decoherence are discussed.
  arXiv  Detail & Related papers  (2021-07-14T09:31:17Z)
• Local Operator Entanglement in Spin Chains [0.0]
  Local perturbations can affect the entire quantum system. quantum computers employ non-equilibrium processes for computations. In this paper, we investigate the evolution of bi- and tripartite operator mutual information of the time-evolution operator and the Pauli spin operators.
  arXiv  Detail & Related papers  (2020-12-29T05:11:28Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.