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Distinguishability of states.
Say you are given a state W) that is either |0) or |1) but you don’t know which. You
can distinguish the two via a measurement in the {|0) , |1)} basis. 51) But what if W) is either |0) or |+) (with equal probability)? Give the protocol that dis-
tinguishes the two states with with a failure probability of sin2(§) % .146. Show explicitly that your protocol achieves this failure probability.
Extra Credit: Prove that this is optimal. b) What is the failure probability for distinguishing IO) from |—|—) if you measure in the
{ID} , |1)} basis?
 
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