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Does measurement violate unitarity?

  1. Feb 15, 2016 #1
    I am taking my first semester of QM so excuse my question if it is way off mark, totally wrong, or very well known.

    As I understand it, one of the postulates of QM are that states evolve unitarily, a consequence (but not THE defining feature) of unitary transformations is that they are invertible.

    Consider some system in state ∑ αii > where |Ψi > are the eigenstates of some observable. Now if I measure my system, then after the measurement the state will be |Ψi > i.e. it will be entirely in that state in which I found it to be.

    If I am correct, then we can represent this by the transformation (1/αi)Pi where Pi is the projection onto the ith eigenstate and (1/αi) rescales it so that <Ψ|Ψ> = 1.

    The problem is that projections arent unitary. In general they arent even invertable. So am I wrong about measurements violating unitarity? Is unitary transformations not a strict requirement?

  2. jcsd
  3. Feb 15, 2016 #2


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    Staff: Mentor

  4. Feb 15, 2016 #3


    Staff: Mentor


    However when entangled with other systems that can break untitary evolution by turning a pure state into an effective mixed state.

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