PHYS 455 Short Answers to Homework III

(b) 〈σ Ax 〉 = tr σ Ax ρ A = 0. Similarly 〈σ Bx 〉 = 〈σ Cx 〉 = 0.(c) Call these probabilities as p +++ , p +−− , p −+− and p −−+ . Then, sum of probabilitiesrule and the known expectation values computed above can be written as1 = p +++ + p +−− + p −+− + p −−+ ,〈σ Ax 〉 = 0 = p +++ + p +−− − p −+− − p −−+ ,〈σ Bx 〉 = 0 = p +++ − p +−− + p −+− − p −−+ ,〈σ Cx 〉 = 0 = p +++ − p +−− − p −+− + p −−+ .Solving these we get p +++ = p +−− = p −+− = p −−+ = 1/4.4