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Generic emergence of objectivity of observables in infi nite dimensions

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


Marco Piani


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.

Journal Article Type Article
Publication Date Oct 17, 2018
Print ISSN 0031-9007
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 121
Issue 16
Article Number 160401
APA6 Citation Knott, P. A., Tufarelli, T., Piani, M., & Adesso, G. (2018). Generic emergence of objectivity of observables in infi nite dimensions. Physical Review Letters, 121(16), doi:10.1103/PhysRevLett.121.160401. ISSN 0031-9007
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