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We formulate entropic measurements uncertainty relations (MURs) for aspin-1/2 system. When incompatible observables are approximatively jointlymeasured, we use relative entropy to quantify the information lost inapproximation and we prove positive lower bounds for such a loss: there is anunavoidable information loss. Firstly we allow only for covariant approximatejoint measurements and we find state-dependent MURs for two or three orthogonalspin-1/2 components. Secondly we consider any possible approximate jointmeasurement and we find state-independent MURs for two or three spin-1/2components. In particular we study how MURs depend on the angle between twospin directions. Finally, we extend our approach to infinitely manyincompatible observables, namely to the spin components in all possibledirections. In every scenario, we always consider also the characterization ofthe optimal approximate joint measurements.

Uncertainty relations and information loss for spin-1/2 measurements