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My question is partially motivated by this discussion. Suppose we have a pure state that is in a superposition for a certain basis, e.g. ##\left|\psi\right\rangle=\alpha\left| 0\right\rangle+\beta\left| 1\right\rangle##. Now a colleague of ours measures the state with respect to that basis, but does not tell us the result. From his point of view, he ends up with a pure state (say ##\left| 0\right\rangle##), from our point of view we have a mixed state ##\rho=\left|\alpha\right|^2 \left| 0\right\rangle\left\langle 0\right|+\left|\beta\right|^2 \left| 1\right\rangle\left\langle 1\right|##.

But what kind of state do we end up with if our colleague doesn't even tell us if he performed the measurement at all?

Or, as a follow-up question, if he doesn't tell us in which basis he measured?

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# What state do we have if we don't know if a measurement was performed?

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