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We discuss the information entropy for a general open pointer-basedsimultaneous measurement and show how it is bound from below. This entropicuncertainty bound is a direct consequence of the structure of the entropy andcan be obtained from the formal solution of the measurement dynamics.Furthermore, the structural properties of the entropy allow us to give anintuitive interpretation of the noisy influence of the pointers and theenvironmental heat bath on the measurement results.

Entropic uncertainty bound for open pointer-based simultaneous measurements of conjugate observables