Partial trace of matrix

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Nikolaos
Nikolaos 2011-7-21
For a given density matrix which originates from a vector which contains four systems, i want to compute the reduced density matrix for each of the four subsystem. (i.e. I have a density matrix which has constructed from four subsystem outer products and I want to compute the partial trace of this matrix for each one of those subsystems).
I. I was wondering if there is an efficient way to do this

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Jean-Daniel
Jean-Daniel 2011-8-22

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Nikolaos
Nikolaos 2011-10-25
thx a lot.. but the problem is that this is not working for all cases. For example if you have tri-partite or four-partite systems. This is my way of making a partial trace of the initial matrix pall of dimensions 100x100 into the partial matrix pred of dimensions 10x10 according to pred(i,j)= Sum_ijkl pall(i,j,k,l)
red=zeros(10)
pd= reshape(pall, 10,10,10,10)
for ii=1:10
for jj=1:10
for mm=1:10
pred(ii,jj)=pred(ii,jj)+pd(ii,mm,jj,mm)
end
end
end

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