Past exam of the laser science and quantum information processing course of the University of Oxford / 2019 / 4 / a / ii

Bob knows the initial amplitudes and the measurement basis but not its result, so he averages the two conditional states:The initial matrix had off-diagonal entries $\alpha {\beta }^{\ast }$ and ${\alpha }^{\ast }\beta$, which the unread measurement removes. Alice's description is conditioned on an available record; Bob's is the nonselective projective measurement mixture. Averaging Alice's records gives exactly Bob's predictions, and communicating the result lets him make the same conditional update. This is a difference of conditioning information, not two inconsistent physical state assignments.