Multiple observations of quantum systems

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Let us assume a following scenario: In a state of a quantum system one qubit is encoded. The first observer has no prior knowledge about the state of the qubit. He performs an optimal measurement on the system and based on the measured data he estimates the state on the qubit. After performing the measurement the first observer leaves the measured quantum system in a lab. I will study the question whether the second observer who has no knowledge about the measurement setup and the measurement outcome of the first observation can learn anything about the original preparation of the qubit.