Von neumann entropy, log(P) ?

  • Thread starter trosten
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  • #1
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Main Question or Discussion Point

Let P be a density matrix. Then the von neumann entropy is defined as
S(P) = -tr(P*log(P))

But how is log(P) defined ?

--edit--
found the answer. the trace is independent of representation so that if P is diagonalized with eigenvalues {k} then S(P) = H({k}) where H is the shannon entropy.
 
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Answers and Replies

  • #2
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[tex]ln(P) = -\sum_{n=1}^\infty \frac{1}{n}(I-A)^n[/tex]
 
  • #3
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trosten said:
found the answer. the trace is independent of representation so that if P is diagonalized with eigenvalues {k} then S(P) = H({k}) where H is the shannon entropy.
right. Usually easier by the way !
 
  • #4
dextercioby
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The definition is really

[tex] S:=-k\langle \ln\hat{\rho}\rangle_{\hat{\rho}} [/tex]

,quite similar to Gibbs' entropy.

Daniel.
 

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