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Measurement problem query

  1. Feb 18, 2012 #1
    In the measurement ansatz below, must the state |O,ready> be orthogonal to |O,reads up> and |O,reads down>]?

    |+x> |O,ready> =1/(sqrt2)[|+z> + |-z>] |O,ready> (1)

    ---------→ 1/(sqrt2)[|+z> + |-z>] |O,ready> (2)


    --------→ 1/(sqrt2)[|+z>|O,reads up> + |-z>|O,reads down>] (3)


    If |O,ready> = [a|O,reads up> + b|O,reads down>] was applied to (2) then it would give an entangled state and if a,b were functions of time then a suitable a and b can't be found that a hamiltonian could reach since

    1/(sqrt2)[|+z> + |-z>] |O,ready>
    = 1/(sqrt2)[|+z> + |-z>] [a|O,reads up> + b|O,reads down>]

    =1/(sqrt2)(a|+z>|O,reads up>+b|+z>|O,reads down>+a|-z>|O,reads up>+b|-z|O,reads down>) which cannot equal (3) for any a,b.

    Am I correct here?
    Many thanks for any help
     
    Last edited: Feb 18, 2012
  2. jcsd
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