5. Some mixed-state state distinguishing problems [8 points, 4 each].

Consider the following state distinguishing problems, where you are given the state on

the left or the right (each, with probability) and your goal is to correctly guess which of

the two states it is. In each case, give the maximum possible success probability possible

and describe the measurement procedure that attains it:

(a)

(b)

state (0)

state (0)

VS.

VS.

state

state

1)

with prob.

with prob.

10) with prob.

+) with prob.