How to transform this problem into SOCP

when I read a paper i met this problem
how can I transform this into SOCP thanks! I think the most important thing is the Hermitian matrices. It is divided into positive semidefinite matrix and negative semidefinite matrix. SO i don’t konw how to sovle it in matlab codes THanks again!

This question is unrelated to CVX. So you should ask at stack exchange or similar forum.

THANKS for your answer lol