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Quantum Physics

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Consider the observable M that corresponds to a measurement in the sign basis where the measurement value is 3 if the outcome is + and -2 if the outcome is -

A)Write M in the standard basis.

B)If M is the Hamiltonian acting on a qubit which is in the state |phy(0)> = |0> at time 0 , what is the state of the qubit at time t ? Assume that you are working in units such that h_bar=1 . You may use e and t in your answer.

C)Now you perform an X measurement on the qubit at time 0 . What is the expected value of your measurement?

D)What if you perform the above measurement at time t=4pi/3 instead? What is the expected value of your measurement?

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