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Mixture of pure states

  • #1

Homework Statement


Let q be a mixed state which we mix from pure states.
What are the weights we must take for the pure states, respectively? Let us
start the solution with the two-state system.

The Attempt at a Solution


My problem is I can't decypher what the problem actually is, from my knowledge a mixed state is any combination of (assume there's a discrete collection of them) pure states summed with weights that add to 1 so at best we get a n-1 dimensional plane of solutions (for n pure states).
So I think I'm seeing this problem incorrectly, could someone push me in the right direction?
 

Answers and Replies

  • #2
196
22
I think you more or less answered the question, such as it is.

You should probably look up the "Bloch sphere" (or Bloch ball) - it's a neat way of visualizing the mixed states of a 2-state system.
 
  • #3
196
22
at best we get a n-1 dimensional plane of solutions (for n pure states).
The space of the mixed states is actually bigger than this - for example with a 2-state system we can build a density matrix using the 4 objects |0><0|, |0><1|, |1><0| and |1><1|, subject to the constraint that the trace has to be 1. So the mixed states of a qubit live in a 3-dimensional space.

(not sure if that's what you meant)
 

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