a) (10 points for 5383/10 points for 7383) If the messages are of variable length,comprised of strings of the symbols, and are all equally likely, compute the density matrix of the alphabet, pë, using the computational basis in your intermediate calculations. Show all intermediate calculations and clearly state all assumptions.

d) (15 points for 5383/10 points for 7383) Assume the symbol |) is measured with the Observable A as given below. What is/are the possible measurement outcome(s)? And what is/are the possible “collapsed” state(s) associated with the outcome(s)? And, what are the probabilities that the measured state(s) collapse for each possible collapsed state(s)? \mathbf{A}=\left[\begin{array}{cc}

0 & -i \\

i & 0

\end{array}\right]