Generic emergence of objectivity of observables in infinite dimensions

Paul A. Knott, Tommaso Tufarelli, Marco Piani, Gerardo Adesso

Research output: Contribution to journalLetter

3 Citations (Scopus)

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.
LanguageEnglish
Article number160401
Number of pages6
JournalPhysical Review Letters
Volume121
Issue number16
DOIs
Publication statusPublished - 17 Oct 2018

Fingerprint

norms
harmonic oscillators
set theory
energy
quantum mechanics
cut-off
theorems
diamonds
fragments
probes

Keywords

  • quantum Darwinism
  • Gaussian states
  • quantum substrates

Cite this

Knott, Paul A. ; Tufarelli, Tommaso ; Piani, Marco ; Adesso, Gerardo. / Generic emergence of objectivity of observables in infinite dimensions. In: Physical Review Letters. 2018 ; Vol. 121, No. 16.
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Generic emergence of objectivity of observables in infinite dimensions. / Knott, Paul A.; Tufarelli, Tommaso; Piani, Marco; Adesso, Gerardo.

In: Physical Review Letters, Vol. 121, No. 16, 160401, 17.10.2018.

Research output: Contribution to journalLetter

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AU - Tufarelli, Tommaso

AU - Piani, Marco

AU - Adesso, Gerardo

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N2 - 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.

AB - 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.

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