SolutionQCQINielsenChuang

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stilnat

Exercise 2.63

4

We actually need to prove the existence of unitaries $U_m$, not just verify the correctness of the formula $M_m = U_m\sqrt{E_m}$. So, the correct solution is something like this: Suppose...

dandanua

Exercise 2.64

2

The actual solution is not too hard (though I also struggled a bit). Let $1 \le k \le m$ and denote $H = span\{\phi_1,...,\phi_m \}$, $H_k = span\{\phi_1,...,\phi_{k-1}, \phi_{k+1},...,\phi_m \}$....

dandanua

The statement in the textbook can be proven correct using Exercise 9.4.

gouguxian