Hi everyone,

I was wondering if it was possible to optimize over the quantum entropy cone natively in JuMP.

If you need a reminder, the cone is

\{(X_1, X_2, X_3): X_1 \preceq X_2^{\frac{1}{2}} \log(X_2^{\frac{-1}{2}}X_3 X_2^{\frac{-1}{2}})X_2^\frac{1}{2}\},

where \log(X) denotes the matrix logarithm and X^\frac{1}{2} denotes the square root of a matrix. I would also be ok with a way of optimizing over the trace of X_1, since this seems to be considerably cheaper and would suit for the problem I have in mind.

As far as I can tell, the two ways of doing this are (a) to use the package CVXQUAD in Matlab, or (b) to use the Domain Driven Solver package in Matlab. This means that it is possible to optimize over this cone in Julia using MATLAB.jl to call Matlab, but I can’t find a native Julia solution in the docs.

Thanks!