Multi-observable Uncertainty Relations in Product Form of Variances

Abstract

We investigate the product form uncertainty relations of variances for $n(n\ge 3)$ 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.

arXiv comment7 pages, 3 figures in Scientific Reports 2016

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• Uncertainty from the Aharonov-Vaidman Identity
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• A Universal Quantum Certainty Relation for Arbitrary Number of Observables
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