Find a 4x4 unitary matrix U such that u = e^iA

=T Define \u) = {(1, -1, -1, 1]" and A = 7 \) (ul. The r is not a typoso A is not a density matrix but it remains Hermitian. Find a 4 x 4 unitary matrix U such that U = eiA. (Possibly up to multiplying by a unit scalar, U is a matrix seen in the course.) Verify your calculation by showing how if U were given, one can obtain A. -1 -1 1 -1 1 - 1 -1 1 1 1 1 Now for an exercise in the other direction, take U Find a Hermi- -1 1 tian matrix A such that U = eiA. (Note that U is not symmetric, so the procedure in section 18.1 will introduce complex entries even though U has none. The latter matrix U comes from the recent Nature paper Markiewicz et al. in E.R.s presentation on interferometers, but this exercise is not directly connected to the paper. It is also "yucky but only 12 pts.)