Multi-observable Uncertainty Relations in Product Form of Variances

Hui-Hui Qin, Shao-Ming Fei, and Xianqing Li-Jost

Contact the author: Please use for correspondence this email.
Submission date: 05. Aug. 2016
Pages: 14
published in: Scientific Reports, 6 (2016), art-no. 31192 
DOI number (of the published article): 10.1038/srep31192
Bibtex
Download full preprint: PDF (217 kB)

Abstract:
We investigate the product form uncertainty relations of variances for n(n ≥ 3) quantum observables. In particular, tight uncertainty relations satisfied by three observables has been derived, which is shown to be better than the ones derived from the strengthened Heisenberg and the generalized Schrödinger uncertainty relations, and some existing uncertainty relation for three spin-half operators. Uncertainty relation of arbitrary number of observables is also derived. As an example, the uncertainty relation satisfied by the eight Gell-Mann matrices is presented.