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Pure states and mixtures

  1. Nov 14, 2013 #1

    naima

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    Is there a way to write p1 |v1> + p2 |v2> if it is not a pure state but a mixture?
    thanks.
     
  2. jcsd
  3. Nov 14, 2013 #2
    If it is a true classical ensemble then no. However, if it's something that you got from tracing over unobserved degrees of freedom then yes. The representation is then the original pure state on the larger space.

    Cheers,

    Jazz
     
  4. Nov 14, 2013 #3

    naima

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    My question is about notations.
    How to write correctly such a mixture?
     
  5. Nov 14, 2013 #4
    Mixtures are hermitian operators or matrices. You can construct them from state vectors by taking a convex sum of their outer products. So for example

    [itex]
    \rho = a^* a \left|\psi\rangle \langle\psi\right| + b^* b \left|\phi\rangle \langle\phi\right|
    [/itex]
     
  6. Nov 14, 2013 #5

    naima

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    Ok
    thank you
    I did not realize that i could write it in this way.
     
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