Uncertainty relations for any multi observables

Jinchuan Hou; Kan He

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arXiv · 1601.06338

Uncertainty relations for any multi observables

Jinchuan Hou·Kan He

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Abstract

Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal uncertainty relation for any $k$ observables, of which the formulation depends on the even or odd quality of $k$. This universal uncertainty relation is tight at least for the cases $k=2n$ and $k=3$. For two observables, the uncertainty relation is exactly a simpler reformulation of Schrödinger's uncertainty principle.

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Jinchuan Hou, Kan He. 2016-01-24. Uncertainty relations for any multi observables. https://arxiv.org/abs/1601.06338

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