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Generic Emergence of Objectivity of Observables in Infinite Dimensions
Paul A Knott1, Tommaso Tufarelli1, Marco Piani2
1Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems (CQNE), School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
Physical Review Letters
|November 3, 2018
Summary
Quantum Darwinism explains objective information in quantum mechanics. This study extends this theory to infinite-dimensional systems, crucial for practical applications like harmonic oscillators.
Area of Science:
- Quantum physics
- Quantum information theory
Background:
- Quantum Darwinism explains how objective classical information emerges from quantum systems.
- Previous work established this for finite-dimensional systems, excluding many practical scenarios.
Purpose of the Study:
- Extend the theory of Quantum Darwinism to infinite-dimensional quantum systems.
- Investigate the emergence of objectivity in systems with infinite dimensions.
Main Methods:
- Developed a modified diamond norm for quantifying channel distinguishability in infinite dimensions.
- Proved two theorems bounding the emergence of objectivity.
Main Results:
- Objectivity emerges in infinite dimensions for systems with finite mean energy.
- Objectivity is also shown for systems with exponential energy cutoffs, including Gaussian states.
Conclusions:
- The study successfully extends Quantum Darwinism to infinite-dimensional systems.
- Provides a theoretical framework applicable to realistic quantum systems like harmonic oscillators.
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