Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 15E / c / iii

Table of contents
- Solution iii

Solution

The operator

F

maps the computational orthonormal basis

{∣ j ⟩}

to the orthonormal basis

{∣ ϕ_{j} ⟩}

. It therefore preserves inner products and is surjective, so

F^{†} F = F F^{†} = I

and

F

is unitary.

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