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Schrödinger's cat, pure or mixed state?

  1. Mar 15, 2012 #1
    The usual description of Schrödinger's cat is that after being placed in the box, Schrödinger's cat in a superposition state of being alive and dead. Sometimes, I see this written as:
    [itex]\mid \Psi \rangle=\frac{1}{\sqrt{2}}(\mid alive \rangle+\mid dead \rangle)[/itex]
    This is representing a particular pure state which is distinctly different from
    [itex]\mid \Psi' \rangle=\frac{1}{\sqrt{2}}(\mid alive \rangle-\mid dead \rangle)[/itex]
    In some sense, these are different rotations of the alive-dead spinor.
    But, should this be more properly treated as a density matrix?
    [itex]\begin{bmatrix} 1/2 & 0 \\ 0 & 1/2 \end{bmatrix}[/itex]
    That is, we have incomplete information about the Schrödinger's cat's exact state, which is significantly less mysterious than claiming the cat is alive+dead.

    We could, for example, construct a Schrödinger box by loading an ampoule with poison, and triggering the poison with a photon detector which is behind a polarizer and a photon source. The photon source emits randomly polarized light. The photon polarization is in a mixed state, so the cat should be, too. Can we actually construct a pure state of cat actually be in a pure state of alive+dead?
     
  2. jcsd
  3. Mar 15, 2012 #2

    Demystifier

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    Science Advisor

    You are right, Schrodinger cat is in the mixed state. The photon is also in the mixed state. But the cat, photon, photon-detector, and their environment TOGETHER are in a pure state.
     
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