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Density operator of unknown system

  1. Apr 20, 2013 #1
    1. The problem statement, all variables and given/known data
    What is the density operator (statistical operator) of a system about which nothing is known?

    2. Relevant equations

    [itex]\hat{\rho} = \sum p_{i} |i\rangle\langle i|[/itex]

    3. The attempt at a solution

    If nothing is known about a system we must assume something in order to make worthwhile statements about it. So if no one state can be preferred over another then it seems a normal distribution of states is likely. This means for N states the [itex]p_{i} = \frac{1}{N}[/itex]

    Putting this in the general definition of density operator gives

    [itex]\hat{\rho} = \frac{1}{N} \sum |i\rangle\langle i| = \frac{1}{N}\cdot \hat{1}[/itex]

    Really?
     
  2. jcsd
  3. Apr 21, 2013 #2

    dextercioby

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    Looks good to me.
     
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