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Why does "tracing out" work

  1. Oct 14, 2014 #1


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    Gold Member

    Hi Pf
    I am looking for the reason why after an interaction "tracing out" the external dof of the system gives the density matrix of the particle.
    I looked in Ballentine if it comes from an axiom but i did not find (one occurence for partial trace)
    I have the tool but i have not the reason why it is a good tool.
  2. jcsd
  3. Oct 14, 2014 #2


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    Science Advisor

    Let the whole system S be divided into A and B, where we observe A and trace out B. You write the observable on the whole system ##O_{S} = O_{A} \otimes I_{B}##, and apply the Born rule to the whole system, and the reduced density matrix should pop out.
  4. Oct 15, 2014 #3


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    Think of tracing out as averaging over unobserved degrees of freedom, which is akin to the concept of marginal probability:
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