Error tradeoff uncertainty relations for three observables

Heisenberg’s uncertainty principle is originally represented by the tradeoff relations between the error of measuring an observable A and the consequential disturbance to the value of another observable B with respect to a particular quantum state. Many different error-disturbance tradeoff relations have been proposed and experimentally tested in various scenarios. The error-disturbance uncertainty relations is incorporated into multiparameter estimation theory recently, but they are all the tradeoff relations between the errors of measuring two observables. Here, we derive the error-disturbance tradeoff relations for three observables A,  B and C and demonstrate that the new relation is violated, while the relations derived from triple of two observables A and B, A and C and B and C directly are valid by some examples.