Quantum scrambling of observable algebras

• URL: http://arxiv.org/abs/2107.01102v3
• Date: Tue, 8 Mar 2022 02:14:02 GMT
• Title: Quantum scrambling of observable algebras
• Authors: Paolo Zanardi
• Abstract summary: quantum scrambling is defined by how the associated physical degrees of freedom get mixed up with others by the dynamics. This is accomplished by introducing a measure, the geometric algebra anti-correlator (GAAC) of the self-orthogonalization of the commutant of $cal A$ induced by the dynamics. For generic energy spectrum we find explicit expressions for the infinite-time average of the GAAC which encode the relation between $cal A$ and the full system of Hamiltonian eigenstates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we describe an algebraic/geometrical approach to quantum scrambling. Generalized quantum subsystems are described by an hermitian-closed unital subalgebra $\cal A$ of operators evolving through a unitary channel. Qualitatively, quantum scrambling is defined by how the associated physical degrees of freedom get mixed up with others by the dynamics. Quantitatively, this is accomplished by introducing a measure, the geometric algebra anti-correlator (GAAC), of the self-orthogonalization of the commutant of $\cal A$ induced by the dynamics. This approach extends and unifies averaged bipartite OTOC, operator entanglement, coherence generating power and Loschmidt echo. Each of these concepts is indeed recovered by a special choice of $\cal A$. We compute typical values of GAAC for random unitaries, we prove upper bounds and characterize their saturation. For generic energy spectrum we find explicit expressions for the infinite-time average of the GAAC which encode the relation between $\cal A$ and the full system of Hamiltonian eigenstates. Finally, a notion of ${\cal A}$-chaoticity is suggested.

Related papers

• Long-time Quantum Scrambling and Generalized Tensor Product Structures [0.0]
  We study the long-time properties of the out-of-time-order-correlator ("$mathcalA$-OTOC") We perform the minimization of the $mathcalA$-OTOC long-time average both analytically and numerically. We conjecture and provide evidence for a general structure of the algebra that minimizes the average for non-resonant Hamiltonians.
  arXiv  Detail & Related papers  (2023-12-20T19:21:06Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• Coherence generation, symmetry algebras and Hilbert space fragmentation [0.0]
  We show a simple connection between classification of physical systems and their coherence generation properties, quantified by the coherence generating power (CGP) We numerically simulate paradigmatic models with both ordinary symmetries and Hilbert space fragmentation, comparing the behavior of the CGP in each case with the system dimension.
  arXiv  Detail & Related papers  (2022-12-29T18:31:16Z)
• Quantum teleportation in the commuting operator framework [63.69764116066747]
  We present unbiased teleportation schemes for relative commutants $N'cap M$ of a large class of finite-index inclusions $Nsubseteq M$ of tracial von Neumann algebras. We show that any tight teleportation scheme for $N$ necessarily arises from an orthonormal unitary Pimsner-Popa basis of $M_n(mathbbC)$ over $N'$.
  arXiv  Detail & Related papers  (2022-08-02T00:20:46Z)
• The classical limit of Schr\"{o}dinger operators in the framework of Berezin quantization and spontaneous symmetry breaking as emergent phenomenon [0.0]
  A strict deformation quantization is analysed on the classical phase space $bR2n$. The existence of this classical limit is in particular proved for ground states of a wide class of Schr"odinger operators. The support of the classical state is included in certain orbits in $bR2n$ depending on the symmetry of the potential.
  arXiv  Detail & Related papers  (2021-03-22T14:55:57Z)
• Symmetric distinguishability as a quantum resource [21.071072991369824]
  We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources. We study the resource theory for two different classes of free operations: $(i)$ $rmCPTP_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doubly (CDS) maps acting on $XA$.
  arXiv  Detail & Related papers  (2021-02-24T19:05:02Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)
• Hamiltonian operator approximation for energy measurement and ground state preparation [23.87373187143897]
  We show how to approximate the Hamiltonian operator as a sum of propagators using a differential representation. The proposed approach, named Hamiltonian operator approximation (HOA), is designed to benefit analog quantum simulators.
  arXiv  Detail & Related papers  (2020-09-07T18:11:00Z)
• Conformal bridge between asymptotic freedom and confinement [0.0]
  We construct a nonunitary transformation that relates a given "asymptotically free" conformal quantum mechanical system $H_f$ with its confined, harmonically trapped version $H_c$. We investigate the one- and two-dimensional examples that reveal, in particular, a curious relation between the two-dimensional free particle and the Landau problem.
  arXiv  Detail & Related papers  (2019-12-26T02:45:37Z)

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.