Sum uncertainty relations for arbitrary N incompatible observables

Bin Chen and Shao-Ming Fei

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Submission date: 25. Aug. 2015
Pages: 12
published in: Scientific Reports, 5 (2015), art-no. 14238 
DOI number (of the published article): 10.1038/srep14238
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Abstract:
We formulate uncertainty relations for arbitrary N observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty relations are explicitly derived. These bounds are shown to be tighter than the ones such as derived from the uncertainty inequality for two observables [Phys. Rev. Lett. 113, 260401 (2014)]. Detailed examples are presented to compare among our results with some existing ones.