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One of the basic lessons of quantum theory is that one cannot obtaininformation on an unknown quantum state without disturbing it. Hence, byperforming a certain measurement, we limit the other possible measurements thatcan be effectively implemented on the original input state. It has beenrecently shown that one can implement sequentially any device, either channelor observable, which is compatible with the first measurement [T. Heinosaariand T. Miyadera: Phys. Rev. A Vol 91 (2015), 022110]. In this work we provethat this can be done, apart from some special cases, only when the succeedingdevice is implemented on a larger system than just the input system. This meansthat some part of the still available quantum information has been flown to theenvironment and cannot be gathered by accessing the input system only. Wecharacterize the size of the post-measurement system by determining the classof measurements for the observable in question that allow the subsequentrealization of any measurement process compatible with the said observable. Wealso study the class of measurements that allow the subsequent realization ofany observable jointly measurable with the first one and show that these twoclasses coincide when the first observable is extreme.

The unavoidable information flow to environment in quantum measurements