Generic emergence of objectivity of observables in infinite dimensions

Abstract

Quantum Darwinism posits that information becomes objective whenever multiple observers indirectly probe a quantum system by each measuring a fraction of the environment. It was recently shown that objectivity of observables emerges generically from the mathematical structure of quantum mechanics, whenever the system of interest has finite dimensions and the number of environment fragments is large [F. G. S. L. Brandão, M. Piani, and P. Horodecki, Nature Commun. 6, 7908 (2015)]. Despite the importance of this result, it necessarily excludes many practical systems of interest that are infinite-dimensional, including harmonic oscillators. Extending the study of Quantum Darwinism to infinite dimensions is a nontrivial task: we tackle it here by using a modified diamond norm, suitable to quantify the distinguishability of channels in infinite dimensions. We prove two theorems that bound the emergence of objectivity, first for finite energy systems, and then for systems that can only be prepared in states with an exponential energy cut-off. We show that the latter class of states includes any bounded-energy subset of single-mode Gaussian states.

arXiv comment15 pages, 3 figures

References in corpus (30)

• Decoherence, einselection, and the quantum origins of the classical
• Decoherence, the measurement problem, and interpretations of quantum mechanics
• Fundamental Limits of Repeaterless Quantum Communications
• General Benchmarks for Quantum Repeaters
• Continuous variable quantum information: Gaussian states and beyond
• General Entanglement Breaking Channels
• Quantum Darwinism
• Coding Theorem and Strong Converse for Quantum Channels
• Separable states are more disordered globally than locally
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• Objective properties from subjective quantum states: Environment as a witness
• Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information
• Generic emergence of classical features in quantum Darwinism
• Environment as a Witness: Selective Proliferation of Information and Emergence of Objectivity in a Quantum Universe
• On the quantification of entanglement in infinite-dimensional quantum systems
• Quantum origins of objectivity
• Quantum Darwinism in an Everyday Environment: Huge Redundancy in Scattered Photons
• Quantum Darwinism in a hazy environment
• Quantum Darwinism in quantum Brownian motion: the vacuum as a witness
• The Rise and Fall of Redundancy in Decoherence and Quantum Darwinism
• Energy-constrained diamond norms and their use in quantum information theory
• Application of quantum Darwinism to a structured environment
• Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities
• Non-Markovianity hinders Quantum Darwinism
• Objectivity in non-Markovian spin-boson model
• Dynamical Objectivity in Quantum Brownian Motion
• Dissipation, dephasing and quantum Darwinism in qubit systems with random unitary interactions
• Strong quantitative benchmarking of quantum optical devices
• Objectivisation In Simplified Quantum Brownian Motion Models
• Analytical studies of Spectrum Broadcast Structures in Quantum Brownian Motion

Cited by in corpus (30)

• Revealing the emergence of classicality in nitrogen-vacancy centers
• Strong Quantum Darwinism and Strong Independence is equivalent to Spectrum Broadcast Structure
• Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
• Quantum Theory of the Classical: Quantum Jumps, Born's Rule, and Objective Classical Reality via Quantum Darwinism
• Eavesdropping on the Decohering Environment: Quantum Darwinism, Amplification, and the Origin of Objective Classical Reality
• Decoherence without entanglement and Quantum Darwinism
• Eliminating Ensembles from Equilibrium Statistical Physics: Maxwell's Demon, Szilard's Engine, and Thermodynamics via Entanglement
• Quantum Darwinism in a structured spin environment
• Redundantly amplified information suppresses quantum correlations in many-body systems
• Quantum Darwinism and non-Markovianity in a model of quantum harmonic oscillators
• Witnessing non-objectivity in the framework of strong quantum Darwinism
• Emergent classicality in general multipartite states and channels
• Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus
• Classifying two-body Hamiltonians for Quantum Darwinism
• Universal structure of objective states in all fundamental causal theories
• Emergence of the Classical from within the Quantum Universe
• Refined diamond norm bounds on the emergence of objectivity of observables
• Amplification, inference, and the manifestation of objective classical information
• Maximal gap between local and global distinguishability of bipartite quantum states
• Quantum Darwinism and the spreading of classical information in non-classical theories
• Observation of Quantum Darwinism and the Origin of Classicality with Superconducting Circuits
• Information Loss Pathways in a Numerically Exact Simulation of a non-Markovian Open Quantum System
• Dressed Quantum Trajectories: Novel Approach to the non-Markovian Dynamics of Open Quantum Systems on a Wide Time Scale
• Compatibility of Quantum Measurements and the Emergence of Classical Objectivity
• On the relation between quantum Darwinism and approximate quantum Markovianity
• Quantitative bounds to propagation of quantum correlations in many-body systems
• Decoherence, quantum Darwinism, and the generic emergence of our objective classical reality
• Commutativity and the emergence of classical objectivity
• Einselection from incompatible decoherence channels
• Thermality versus objectivity: can they peacefully coexist?