Let |) and |p) be single-qubit states. We say that ) and p) are perfectly distinguishable if there exists some unitary V

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Let And P Be Single Qubit States We Say That And P Are Perfectly Distinguishable If There Exists Some Unitary V 1 (201.76 KiB) Viewed 26 times

Let |) and |p) be single-qubit states. We say that ) and p) are perfectly distinguishable if there exists some unitary V such that: Pr (obtain 0 upon measuring V |)) = 1, Pr(obtain 1 upon measuring V |p)) = 1. By considering the quantity: (V¹0) (0|V|6) + (p|v¹|1) (1|V), or otherwise, show that if |ø) and p) are perfectly distinguishable, then (p|o) = 0. Hint: You may find the identity 1 = |0) (0| + |1) (1| useful. [8 marks]