I have seen some people from cvxpy tried to cook up some hacks to include partial trace in a SDP problem, c.f. https://github.com/cvxpy/cvxpy/issues/563. Has there been any effort for CVX? CVXQUAD has some good functions for quantum info but unfortunately lacks the partial trace.
I suppose you can write your own version, and feel free to post it here. You can take advantage of CVX’s multidimensional array capability.
The answer at https://cstheory.stackexchange.com/questions/13948/using-matlabs-cvx-package-for-semidefinite-programming-in-quantum-information provides a link to what perhaps is a partial trace implementation in CVX, but the post is old, and the link is dead.
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Update:
There is a partial trace in QETLAB, written by @Nathaniel_Johnston at https://github.com/nathanieljohnston/QETLAB/blob/master/PartialTrace.m .
Thanks so much for the update! I will take a look at it