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### Fine's theorem for Leggett-Garg tests with an arbitrary number of measurement times

File | Description | Size | Format | |
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1906.04865(final).pdf | Accepted version | 830.89 kB | Adobe PDF | View/Open |

Title: | Fine's theorem for Leggett-Garg tests with an arbitrary number of measurement times |

Authors: | Halliwell, JJ Mawby, C |

Item Type: | Journal Article |

Abstract: | If the time evolution of a quantum system can be understood classically, then there must exist an underlying probability distribution for the variables describing the system at a sequence of times. It is well known that for systems described by a single time-evolving dichotomic variable Q and for which a given set of temporal correlation functions are specified, a necessary set of conditions for the existence of such a probability are provided by the Leggett-Garg (LG) inequalities. Fine's theorem in this context is the nontrivial result that a suitably augmented set of LG inequalities are both necessary and sufficient conditions for the existence of an underlying probability. We present a proof of Fine's theorem for the case of measurements on a dichotomic variable at an arbitrary number of times, thereby generalizing the familiar proofs for three and four times. We demonstrate how the LG framework and Fine's theorem can be extended to the case in which all possible two-time correlation functions are measured (instead of the partial set of two-time correlators normally studied). We examine the limit of a large number of measurements for both of the above cases. |

Issue Date: | 1-Oct-2019 |

Date of Acceptance: | 1-Oct-2019 |

URI: | http://hdl.handle.net/10044/1/81728 |

DOI: | 10.1103/PhysRevA.100.042103 |

ISSN: | 1050-2947 |

Publisher: | American Physical Society |

Start Page: | 042103 – 1 |

End Page: | 042103 – 12 |

Journal / Book Title: | Physical Review A: Atomic, Molecular and Optical Physics |

Volume: | 100 |

Issue: | 4 |

Copyright Statement: | ©2019 American Physical Society |

Keywords: | Science & Technology Physical Sciences Optics Physics, Atomic, Molecular & Chemical Physics BELLS THEOREM QUANTUM Science & Technology Physical Sciences Optics Physics, Atomic, Molecular & Chemical Physics BELLS THEOREM QUANTUM |

Publication Status: | Published |

Open Access location: | https://arxiv.org/pdf/1906.04865.pdf |

Article Number: | ARTN 042103 |

Online Publication Date: | 2019-10-01 |

Appears in Collections: | Physics Theoretical Physics |