Experimental Investigation of Heisenberg Uncertainty Lower Bounds for Three Incompatible Observables at Single-Spin Level

In the light of the Busch, Lathi and Werner proposal, we explore, for the first time, the joint measurements and confirmation of uncertainty relations for three incompatible observables that reflect the original spirit proposed by Heisenberg in 1927. We first develop the error trade-off relations theoretically and then demonstrate the first experimental witness of joint measurements using a single ultracold 40Ca+ ion trapped in a harmonic potential. In addition, we report, that in contrast to the case of two observables, scarifying accuracy of any one of the three observables the rest of two can be measured with ultimate accuracy.