### Abstract

We prove a no-go theorem for a class of hidden variables theories that satisfy parameter independence. Specifically, we show that, assuming two conditions, there are no non-trivial hidden variables models of the quantum predictions for product measurements on two systems in any maximally entangled state in a Hilbert space of dimension at least 3x3. The two conditions are parameter independence and a condition that we call conditional parameter independence. The result is analogous to the recent no-go theorems based on Leggett's inequalities and their generalisations.

Original language | English |
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Title of host publication | Foundations of Probability and Physics |

Subtitle of host publication | 5, Växjö, Sweden 24-27 August 2008 |

Editors | L Accardi, G Adenier, A Khrennikov, C Fuchs, G Jaeger, J A Larsson, S Stenholm |

Place of Publication | Melville, NY, USA |

Publisher | American Institute of Physics |

Pages | 233-240 |

Number of pages | 8 |

ISBN (Print) | 0735406367 , 978-0735406360 |

DOIs | |

Publication status | Published - 19 Apr 2009 |

Event | 5th Conference on Foundations of Probability and Physics - Växjö, Sweden Duration: 24 Aug 2008 → 27 Aug 2008 |

### Publication series

Name | Conference Proceedings |
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Publisher | American Institute of Physics |

Volume | 1101 |

### Conference

Conference | 5th Conference on Foundations of Probability and Physics |
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Country | Sweden |

City | Växjö |

Period | 24/08/08 → 27/08/08 |

### Keywords

- nonlocality
- hidden variables

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## Cite this

Bacciagaluppi, G. (2009). Leggett's theorem without inequalities. In L. Accardi, G. Adenier, A. Khrennikov, C. Fuchs, G. Jaeger, J. A. Larsson, & S. Stenholm (Eds.),

*Foundations of Probability and Physics: 5, Växjö, Sweden 24-27 August 2008*(pp. 233-240). (Conference Proceedings; Vol. 1101). American Institute of Physics. https://doi.org/10.1063/1.3109945