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Given: |Q1> = (cos x)|E1> + (sin x)|E2>

1) Express |Q2> as a superposition of |E1> and |E2> and determine the coefficients:

|Q2> = a|E1> + b|E2>

solution: Since Q is hermitian, the eigenstates are orthogonal ->

<Q1|Q2> = a (cos x) + b (sin x) = 0

=> a = -sin x; b = cos x (up to an overall phase factor - the minus sign could be switched)

2) The system is prepared at t = 0 to be in the state |E1>. It is then measured, first by Alice and then by Bob.

At t = t1, Alice measures Q. What is the probability that the measurement will yield Q1?

Here I will denote the state of the system as |X>

solution: |X(t)> = |E1> exp(-iE1 t / h)

P(Q1) = <Q1|X(t1)><X(t1)|Q1> = (cos x) exp (iE1 t1 /h) <E1|E1> cos (x) exp(-iE1 t1 / h) = (cos x) ^2

3) At t2 > t1 Bob measures Q. Again, determine the probability a measurement will yield Q1 - but consider the following two cases:

case 1) Alice reported that her result was Q1

case 2) Alice did not report the result of her measurement

Here is where I am confused... any help would be greatly appreciated :)

If my post has not met the guidelines, please notify me and i will modify where appropriate.

Thank you