Show is the solver and CVX output. If the solver fails (due to numerical reasons), the objective value and all variable values are meaningless.
Perhaps your problem has poorly scaled (very small or large magnitude) input data?
It appears the code with quantum_rel_entr is commented out. Did you actually use it?
All the help for CVXQUAD is at
and
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 .
As fort how changing the value of snr should affect the optimal objective value, it’s your model (or wherever you got it from), not ours, so you should be the expert on that, not us. We don’t know what 'should" happen.