Generic emergence of objectivity of observables in infinite dimensions

Knott, Paul A. and Tufarelli, Tommaso and Piani, Marco and Adesso, Gerardo (2018) Generic emergence of objectivity of observables in infinite dimensions. Physical Review Letters, 121 (16). 160401. ISSN 1079-7114 (https://doi.org/10.1103/PhysRevLett.121.160401)

[thumbnail of Knott-etal-PRL-2018-Generic-emergence-of-objectivity-of-observables]
Preview
 Text. Filename: Knott_etal_PRL_2018_Generic_emergence_of_objectivity_of_observables.pdf
Accepted Author Manuscript
Download (1MB)| Preview

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. Brandao, 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 mean 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 includes any bounded-energy subset of single-mode Gaussian states.

ORCID iDs

Knott, Paul A., Tufarelli, Tommaso, Piani, Marco ORCID logoORCID: https://orcid.org/0000-0002-4698-9497 and Adesso, Gerardo;
  • Item type:Article
    ID code:65598
    Dates:
    Date
    Event
    17 October 2018
    Published
    26 September 2018
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:02 Oct 2018 09:11
    Last modified:11 Nov 2024 12:07
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/65598
CORE (COnnecting REpositories)