(Maximum score is Problem 1 (50 points): Using density matrices to compute expectation values. Does this make sense? We have seen in class that the density operator p is a useful object to construct, because it allows for the calculation of expectation values of operators in pure or mixed quantum states. For a generic operator , the expectation value (A) in the quantum state described by the density operator is simply the trace of the product of and p. An experimentalist was excited to test in the laboratory the exotic density operator 3 = -|-+z) (+z| | 2) (z| | z) (+z| | + z) (z| for a single spin-1/2 fermion that was suggested by a theorist. Based on the information above, answer the following questions. a) What is the expectation value of $? b) What is the expectation value of y? c) What is the expectation value of ? d) What kind of state does this density operator describe? e) Discuss on physical grounds anything unusual or interesting about the density operator