I assume you're doing Exercise 2.20? What is
Quantum computation and quantum ... - Google Books
I am doing the problem above.
then use the fact that and
eventually you get
how do I invoke the unitary matrix? We know that
Drexel28: in quantum mechanics, "kets", or column vectors (at least in finite-dimensional Hilbert spaces) look like this: whereas "bras", or row vectors in the dual space look like this: A "bracket" is an inner product of a bra with a ket: You can also form a matrix with the outer product thus:
That's correct. Then somehow I am supposed to come up with U_{im} and U_{nj}^{*} but I thought it was the other way around U_{mn} and U_{ij}^{*}.
Then I am supposed to show that they have the same eigenvalues. Similar matrices have the same eigenvalues but I am not sure how relevant that is based on what is given.
Answer is:
which is unclear.