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Multi-observable Uncertainty Relations in Product Form of Variances
Hui-Hui Qin1, Shao-Ming Fei2,3, Xianqing Li-Jost3
1Department of Mathematics, School of Science, South China University of Technology, Guangzhou 510640, China.
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.
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