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Pure mixed entangled confusion

  1. Jan 3, 2010 #1
    I have read quite a bit on here and elsewhere, but am still coming to terms with pure, mixed, entangled and product states.

    I know a state is either mixed or pure, but then is engtaglement a sub-class of being mixed? Or a sub-class of being pure? Or is entangled another name for pure? Or something different altogether?

    Also is a product state another way to say mixed? Is it the opposite to entanged?

    As you can see, I am very confused!

    Thanks in advance of replies posted.
  2. jcsd
  3. Jan 10, 2010 #2


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    Pure state = a projection operator for a 1-dimensional subspace, i.e. an operator of the form [itex]|\psi\rangle\langle\psi|[/itex]
    Mixed state = a density operator (a linear operator satisfying 2.6-2.8) that isn't a pure state

    One way to see if a density operator [itex]\rho[/itex] is pure or not is to compute [itex]\operatorname{Tr}\rho^2[/itex]. The result is =1 if and only if the state is pure. (It's <1 for mixed states).

    Entangled state = a state of a composite system that can't be expressed as a tensor product [itex]|\psi_1\rangle\otimes\cdots\otimes|\psi_n\rangle[/itex] (It would therefore have to be expressed as a linear combination of such tensor products).
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