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We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. Firstly, an uncertainty equality as well as an inequality is formulated, and we demonstrate that the new uncertainty inequality is tighter than other recent uncertainty relations. Then, a proof, that the triviality problem of the product form uncertainty relation can be completely fixed by the obtained uncertainty relation, is presented. Finally, we show that the uncertainty equality can be used as a measure of the mixedness of the system which usually is expensive in terms of resources involved.

Multi-observable uncertainty equality based on the sum of standard deviations in the qubit system