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**20171109URsForLinearCombinations(acceptedbyJPA)**210 KB, PDF document

Journal | Journal of Physics A: Mathematical and Theoretical |
---|---|

Date | Accepted/In press - 24 Nov 2017 |

Date | E-pub ahead of print - 24 Nov 2017 |

Date | Published (current) - 11 Dec 2017 |

Issue number | 2 |

Volume | 51 |

Number of pages | 18 |

Early online date | 24/11/17 |

Original language | English |

For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by N linear combinations of position and momentum observables. The bounds depend on their degree of incompatibility defined by the area of a parallelogram in an N-dimensional coefficient space. Maximal incompatibility occurs if the observables give rise to regular polygons in phase space. We also conjecture a Hirschman-type uncertainty relation for N observables linear in position and momentum, generalizing the original relation which lower-bounds the sum of the position and

momentum Shannon entropies of the particle.

momentum Shannon entropies of the particle.

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