Quantum Darwinism-encoding transitions on expanding trees
arXiv:2312.04284 · doi:10.1103/PhysRevA.109.032226
Abstract
Quantum Darwinism (QD) proposes that classical objectivity emerges from the broadcast of information about a microscopic degree of freedom into multiple fractions of a many-body environment. Such a broadcast of information is in sharp contrast with its scrambling under strong interaction. It was recently shown that quantum dynamics interpolating between broadcasting and scrambling may display sharp phase transitions of information propagation, named QD-encoding transitions. Here, we initiate their systematic study in generic, non-Clifford settings. First, in a general theoretical setup where the information propagation is modeled as an isometry, whose input qudit is entangled with a reference, we propose a probe of the transitions -- the distribution of the density matrix of the reference after measuring an environment fraction. This probe measures the classical correlation between the fraction and the injected information. We then apply the framework to two similar models defined by a tensor network on an expanding tree, modeling a noisy apparatus that attempts to broadcast the component of a spin-half. We derive an exact recursion relation of the density matrix distribution, which we analyze analytically and numerically. As a result we find three phases: QD, intermediate and encoding, and two continuous transitions. The encoding-intermediate transition describes the establishment of nonzero correlation between the reference and a small environment fraction, and can be probed by a ``coarse-grained'' measure of the total spin- of the fraction, which becomes non-Gaussian and symmetry breaking in the intermediate space. The QD-intermediate transition is about whether the correlation is perfect. It must be probed by fined-grained measures, and corresponds to a more subtle symmetry breaking in the replica space.
28 pages, 15 figures, many diagrams; v3: minor revision, matching published version
References in corpus (55)
- Many-Body Physics with Ultracold Gases
- Introducing Quantum Discord
- Chaos and Quantum Thermalization
- The nitrogen-vacancy colour centre in diamond
- Classical, quantum and total correlations
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Many-body localization, thermalization, and entanglement
- Average Entropy of a Subsystem
- Black holes and the butterfly effect
- Improved Simulation of Stabilizer Circuits
- Black holes as mirrors: quantum information in random subsystems
- Entanglement renormalization
- Fast Scramblers
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Quantum Information and Relativity Theory
- The Einstein-Podolsky-Rosen paradox: from concepts to applications
- Quantum Darwinism
- Theory of the phase transition in random unitary circuits with measurements
- Measurement-induced criticality in random quantum circuits
- Random Quantum Circuits
- Quantum Decoherence
- Dynamical purification phase transitions induced by quantum measurements
- Dynamical Critical Phenomena in Driven-Dissipative Systems
- Scalable probes of measurement-induced criticality
- Observation of measurement-induced quantum phases in a trapped-ion quantum computer
- A strong no-go theorem on the Wigner's friend paradox
- Objective properties from subjective quantum states: Environment as a witness
- Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information
- Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
- Measurement-induced criticality in (2+1)-d hybrid quantum circuits
- Planckian Dissipation in Metals
- Entanglement renormalization and topological order
- A no-go theorem for observer-independent facts
- Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system
- A branching random walk seen from the tip
- Collision models in open system dynamics: A versatile tool for deeper insights?
- Cross Entropy Benchmark for Measurement-Induced Phase Transitions
- The Rise and Fall of Redundancy in Decoherence and Quantum Darwinism
- Revealing the emergence of classicality in nitrogen-vacancy centers
- Strong Quantum Darwinism and Strong Independence is equivalent to Spectrum Broadcast Structure
- Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes
- Experimental signature of Quantum Darwinism in photonic cluster states
- Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
- Roads to objectivity: Quantum Darwinism, Spectrum Broadcast Structures, and Strong quantum Darwinism -- a review
- Eavesdropping on the Decohering Environment: Quantum Darwinism, Amplification, and the Origin of Objective Classical Reality
- Collisional unfolding of quantum Darwinism
- Measurement-induced phase transitions on dynamical quantum trees
- Objectivity (or lack there of): a comparison between predictions of quantum Darwinism and spectrum broadcast structure
- Quantum Darwinism in a structured spin environment
- Redundantly amplified information suppresses quantum correlations in many-body systems
- Renormalization group for measurement and entanglement phase transitions
- Pointer states and quantum Darwinism with 2-body interactions
- A Solvable Model of Quantum Darwinism-Encoding Transitions
- Clusters in the critical branching Brownian motion