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arXiv · 1701.01072

A Stronger Multi-observable Uncertainty Relation

Qiu-Cheng Song·Jun-Li Li·Guang-Xiong Peng·Cong-Feng Qiao
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Abstract

Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty relation. Here we present a variance-based sum uncertainty relation for $N$ incompatible observables stronger than the simple generalization of the uncertainty relation for two observables derived by Maccone and Pati [Phys. Rev. Lett. {\bf113}, 260401 (2014)]. Further comparisons of our uncertainty relation with other related ones for spin-$\frac{1}{2}$ and spin-$1$ particles indicate that the obtained uncertainty relation gives a better lower bound.

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Qiu-Cheng Song, Jun-Li Li, Guang-Xiong Peng, Cong-Feng Qiao. 2017-01-04. A Stronger Multi-observable Uncertainty Relation. https://doi.org/10.1038/srep44764

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