Scrambling of Algebras in Open Quantum Systems

• URL: http://arxiv.org/abs/2206.02033v5
• Date: Sat, 29 Apr 2023 05:35:31 GMT
• Title: Scrambling of Algebras in Open Quantum Systems
• Authors: Faidon Andreadakis, Namit Anand, Paolo Zanardi
• Abstract summary: We introduce an algebraic OTOC ($mathcalA$-OTOC) that allows us to study information scrambling of quantum subsystems under quantum channels. For closed quantum systems, this framework was recently employed to unify quantum information-theoretic notions of operator entanglement, coherence-generating power, and Loschmidt echo. Our numerical results reveal connections with many-body scars and the stability of decoherence-free subspaces.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many quantitative approaches to the dynamical scrambling of information in quantum systems involve the study of out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us to study information scrambling of generalized quantum subsystems under quantum channels. For closed quantum systems, this algebraic framework was recently employed to unify quantum information-theoretic notions of operator entanglement, coherence-generating power, and Loschmidt echo. The main focus of this work is to provide a natural generalization of these techniques to open quantum systems. We first show that, for unitary dynamics, the $\mathcal{A}$-OTOC quantifies a generalized notion of information scrambling, namely between a subalgebra of observables and its commutant. For open quantum systems, on the other hand, we find a competition between the global environmental decoherence and the local scrambling of information. We illustrate this interplay by analytically studying various illustrative examples of algebras and quantum channels. To complement our analytical results, we perform numerical simulations of two paradigmatic systems: the PXP model and the Heisenberg XXX model, under dephasing. Our numerical results reveal connections with many-body scars and the stability of decoherence-free subspaces.

Related papers

• Quantum steering ellipsoids and quantum obesity in critical systems [0.0]
  Quantum obesity (QO) is new function used to quantify quantum correlations beyond entanglement. We show that QO is a fundamental quantity to observe signature of quantum phase transitions.
  arXiv  Detail & Related papers  (2023-12-19T19:14:08Z)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial [0.0]
  This tutorial introduces the physics of quantum information scrambling in quantum many-body systems. The goals are to understand how to precisely quantify the spreading of quantum information and how causality emerges in complex quantum systems.
  arXiv  Detail & Related papers  (2022-02-14T22:04:12Z)
• A thorough introduction to non-relativistic matrix mechanics in multi-qudit systems with a study on quantum entanglement and quantum quantifiers [0.0]
  This article provides a deep and abiding understanding of non-relativistic matrix mechanics. We derive and analyze the respective 1-qubit, 1-qutrit, 2-qubit, and 2-qudit coherent and incoherent density operators. We also address the fundamental concepts of quantum nondemolition measurements, quantum decoherence and, particularly, quantum entanglement.
  arXiv  Detail & Related papers  (2021-09-14T05:06:47Z)
• Tracing Information Flow from Open Quantum Systems [52.77024349608834]
  We use photons in a waveguide array to implement a quantum simulation of the coupling of a qubit with a low-dimensional discrete environment. Using the trace distance between quantum states as a measure of information, we analyze different types of information transfer.
  arXiv  Detail & Related papers  (2021-03-22T16:38:31Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Information Scrambling and Chaos in Open Quantum Systems [0.0]
  "Open bipartite OTOC" can be treated in an exact analytical fashion and is shown to amount to a distance between two quantum channels. Our analytical form unveils competing entropic contributions from information scrambling and environmental decoherence. As a physical application we numerically study dissipative many-body spin-chains and show how the competing entropic effects can be used to differentiate between integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2020-12-24T08:55:52Z)
• Quantum information spreading in a disordered quantum walk [50.591267188664666]
  We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
  arXiv  Detail & Related papers  (2020-10-20T20:03:19Z)
• Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
  dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
  arXiv  Detail & Related papers  (2020-07-23T19:05:56Z)

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.