Talk:Quantum operation: Difference between revisions

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imported>Hendra I. Nurdin
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imported>Paul Wormer
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== Comment on pure v. impure states ==
In usual textbooks of QM one distinguishes pure and impure states (at the moment I do not have access to any text on QM, I'm writing from memory, so I cannot quote sources). I would write:
:''An impure state of a quantum system is represented on a [[Hilbert space]] <math>\scriptstyle \mathcal{H}</math> by a non-negative definite [[Trace (mathematics)#Infinite-dimensional space|trace class operator]] on <math>\scriptstyle \mathcal{H}</math> with trace equal to one. Such operators are called [[density operator|density operators]].''
After projective measurement the state has become pure, i.e., <math>\scriptstyle \rho'=\frac{P_i \rho P_i}{{\rm tr}(P_i \rho P_i)}</math>, describe a density that is  a delta-function with as peak the pure state &psi;<sub>i</sub>. --[[User:Paul Wormer|Paul Wormer]] 20:36, 11 April 2009 (UTC)

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 Definition:  A mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. [d] [e]
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Comment on pure v. impure states

In usual textbooks of QM one distinguishes pure and impure states (at the moment I do not have access to any text on QM, I'm writing from memory, so I cannot quote sources). I would write:

An impure state of a quantum system is represented on a Hilbert space by a non-negative definite trace class operator on with trace equal to one. Such operators are called density operators.

After projective measurement the state has become pure, i.e., , describe a density that is a delta-function with as peak the pure state ψi. --Paul Wormer 20:36, 11 April 2009 (UTC)

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