5. Suppose that a particle goes through two slits and finds itself in the state (|slit1) + (slit2) ) / v2. An evil spy attempts to measure which slit the particle traverses, but he is not entirely successful. With his measuring device, he manages to create a final state (|slit1) | A) + (slit2) [ B) ) / v2, where A and B are the two possible final states of his device. (a) The probability Pr(x) of finding the particle at some position x on a screen can be calculated by evaluating the expectation value of the projection operator (x) (x). Let us make the simplification that (x) can be represented by N ((slit1) + (slit2)el?), where o serves as a reparametrization of x and N is a prefactor we need not evaluate for the present discussion. The visibility V of an interference fringe is defined as (max-min) /(max+min), where "max" and "min" refer to the maxima and minima of Pr(x). Find the visibility as a function of (A|B) .2 (b) If the spy had been entirely successful in making his measurement, what would that have implied about [A) and [B) and why? Using this result in conjunction with part a, what do you conclude