1. Suppose we have the state =N[(1+i)0+1] (a) What does N have to be to make this a valid quantum state? (b) Suppose I measure in the 0,1 basis. What are the possible outcomes and what are the probabilities of those outcomes? (c) Describe the possible outcomes (with probabilities) for a measurement in the +, basis. (d) Suppose I do a measurement in the 0,1 basis followed by a measurement in the +, basis. Draw the four possible outcomes in a branching tree. What are the total probabilities for getting + or (regardless of the outcome of the first measurement). How does this compare to what you got in part (c)? Why