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Geometry of Uncertainty Relations for Linear Combinations of Position and Momentum

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JournalJournal of Physics A: Mathematical and Theoretical
DateAccepted/In press - 24 Nov 2017
DateE-pub ahead of print - 24 Nov 2017
DatePublished (current) - 11 Dec 2017
Issue number2
Volume51
Number of pages18
Early online date24/11/17
Original languageEnglish

Abstract

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.

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