Generic emergence of objectivity of observables in infinite dimensions

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

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.

Citation

Knott, P. A., Tufarelli, T., Piani, M., & Adesso, G. (2018). Generic emergence of objectivity of observables in infinite dimensions. Physical Review Letters, 121(16), https://doi.org/10.1103/PhysRevLett.121.160401

• Journal Article Type: Article
• Acceptance Date: Sep 26, 2018
• Online Publication Date: Oct 17, 2018
• Publication Date: Oct 19, 2018
• Deposit Date: Oct 11, 2018
• Publicly Available Date: Oct 11, 2018
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 121
• Issue: 16
• Article Number: 160401
• DOI: https://doi.org/10.1103/PhysRevLett.121.160401
• Keywords: Quantum Physics; High Energy Physics - Theory; Mathematical Physics; History and Philosophy of Physics
• Public URL: https://nottingham-repository.worktribe.com/output/1159411
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.160401