The best and most reliable solver for this problem is Mosek, which avoids CVX’s Successive Approximation method. if Mosek is not available to you, follow the advice at CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions
However, Mosek 10.1.10 failed on the few (random) problem instances I tried, with the status of dual ill-posed, which given that Mosek was provided the primal, means that Mosek assessed the problem is dual ill-posed. I will leave the assessment as to why to others.
Note that I have not attempted to check whether your CVX code matches the problem statement in the graphic. But because CVX called the solver, the program is a “legal” CVX program, although whether it is “correct” or good is another matter.