 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2020/quantum-information/3/a/solution

Substitute the promised cardinalities:

\frac{2 ( S _{0} - S _{1} )}{N} = \frac{2}{N} (\frac{3 N}{4} - \frac{N}{4}) = \frac{2}{N} \frac{N}{2} = 1 .

The marked and unmarked subsets also exhaust the computational basis, so

S_{0} + S_{1} = N

; this will ensure that the uniform initial state has unit norm.

 New to topics? Read the docs here!