### Abstract

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.

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 |

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### Keywords

- quantum Darwinism
- Gaussian states
- quantum substrates

### Cite this

*Physical Review Letters*,

*121*(16), [160401]. https://doi.org/10.1103/PhysRevLett.121.160401

}

*Physical Review Letters*, vol. 121, no. 16, 160401. https://doi.org/10.1103/PhysRevLett.121.160401

**Generic emergence of objectivity of observables in infinite dimensions.** / Knott, Paul A.; Tufarelli, Tommaso; Piani, Marco; Adesso, Gerardo.

Research output: Contribution to journal › Letter

TY - JOUR

T1 - Generic emergence of objectivity of observables in infinite dimensions

AU - Knott, Paul A.

AU - Tufarelli, Tommaso

AU - Piani, Marco

AU - Adesso, Gerardo

PY - 2018/10/17

Y1 - 2018/10/17

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.

KW - quantum Darwinism

KW - Gaussian states

KW - quantum substrates

UR - https://journals.aps.org/prl/issues

U2 - 10.1103/PhysRevLett.121.160401

DO - 10.1103/PhysRevLett.121.160401

M3 - Letter

VL - 121

JO - Physical Review Letters

T2 - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 16

M1 - 160401

ER -