You certainly don't need a grad degree to understand the math behind entanglement or basic QM!

"Just" partial differential equations of complex fields for Schrodinger; the fourier transform to shift between, what was it, momentum and position?; matricies and/or quaternions for the Bloch sphere; bra-ket notation; and the Hermitian, Hamiltonian, and Laplacian operators.

Of these, the only one I did in my double maths A-level was matricies and partial differential equations of single dimensional real functions, and the absolute basics of what complex numbers are.

Seems like it needs a degree to me, having tried to teach myself using brilliant.org