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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 infinitedimensional, 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 cutoff. We show that the latter class includes any boundedenergy subset of singlemode Gaussian states.
Nature Commun. 6, 7908 (2015)]. Despite the importance of this result, it necessarily excludes many practical systems of interest that are infinitedimensional, 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 cutoff. We show that the latter class includes any boundedenergy subset of singlemode Gaussian states.
Original language  English 

Article number  160401 
Number of pages  6 
Journal  Physical Review Letters 
Volume  121 
Issue number  16 
DOIs  
Publication status  Published  17 Oct 2018 
Keywords
 quantum Darwinism
 Gaussian states
 quantum substrates
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 2 Finished

Sentient observers in the quantum regime and the emergence of an objective reality
Piani, M.
Foundational Questions Institute FQXi
1/02/17 → 31/07/18
Project: Research

OPERACQC: Operational Characterization of Quantum Correlations
Piani, M. & Daley, A.
1/05/15 → 1/05/17
Project: Research Fellowship