Perspective of log det function, and CVX formulations of related log det problems using Quantum Relative Entropy from CVXQUAD

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Here is how to formulate x\log|I+ xY^{-1}|, x \geq 0,Y \in S^{++}, which is jointly convex in x and Y.

x*log(det(eye(n) + x*inv(Y)))
can be formulated as
quantum_rel_entr(x*eye(n)+Y,Y) + quantum_rel_entr(Y,x*eye(n)+Y)

which turns out to be the quantum (matrix) analog of @Michal_Adamaszek 's scalar formulation
x*log(1+x/y) = rel_entr(x+y,y) + rel_entr(y,x+y)
from Writing x*log(1+x/y)

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