physics

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 −.
Write M in the standard basis.
If M is the Hamiltonian acting on a qubit which is in the state |ψ(0)⟩=|0⟩ at time 0, what is the state of the qubit at time t? Assume that you are working in units such that ℏ=1. You may use e and t in your answer.
Now you perform an X=(0110) measurement on the qubit at time 0. What is the expected value of your measurement?
What if you perform the above measurement at time t=4π3 instead? What is the expected value of your measurement?

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asked by Sam
  1. We have:

    |+> = 1/sqrt(2)[|0> + |1>]

    |-> = 1/sqrt(2)[|0> - |1>]

    M = 3|+><+| - 2 |-><-|

    Insert the above expressions and expand, or just evaluate the matrix elements. E.g.:

    <0|M|0> =

    3<0|+><+|0> - 2 <0|-><-|0> =

    3/2 - 1 = 1/2

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  2. I was able to do part 1 and part 2. I am stuck on
    Now you perform an X=(0110) measurement on the qubit at time 0. What is the expected value of your measurement?
    What if you perform the above measurement at time t=4π3 instead? What is the expected value of your measurement?

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    posted by Sam

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