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I have read the paper "Steady state entanglement between hybrid light-matter qubits", arXiv:0711.1830v2. There, writers obtained density operator in matrix form after solving steady state equation (13). I want to know how one can trace out polaritonic degree of freedom of one of two cavities.

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Hi kate, and welcome to Physics Stack Exchange! This is a very good question. I'm not sure whether anyone who frequents this site has the expertise to answer it, but I hope so. –  David Z Nov 28 '11 at 0:51
    
Are you asking how you reduce the 4 by 4 density matrix for 2 qubits into the 2 by 2 matrix for one qubit? Or do you want something more? –  Ron Maimon Nov 28 '11 at 8:29
    
yes, that is what exactly I want. But in this case, when we want to find reduced density matrix for each of these polaritons I guess we should consider influence of entanglement. I mean each of these polaritons should not have equal density matrix. –  kate Nov 28 '11 at 18:37
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