Homework 2
   Assigned on Oct 4, due Oct 11 in class

   8 problems are from Nielsen/Chuang and two are described explicitly.

   Problems I-VII:  2.53, 2.59, 2.65, 2.66, 2.68, 2.69, 2.77

   Problem VIII.
   Do what's asked in problem 2.64, except that you are allowed to
   specify measurements in any of the forms described in the book or
   in class. You need to substantiate your answer.

   Problem IX.
   Prove that if A is self-adjoint, then exp(iA) and exp(-iA) are unitaries
   (Hint: use Taylor expansion of exp(x) at x=0)

   Problem X.
   Study material in Box 2.3 on p. 87 and Box 3.4 on p. 154
   Show that it is possible two tell two unequal vectors apart
   by quantum measurements if, in addition to what's assumed in Box 2.3,
   (1) you are given an unlimited supply of identical copies of quantum
       systems with the same two vectors
   (2) you are allowed to claim a result if it is correct with probability
       0.999999 (rather than 1.0 as required in Box 2.3)