You haven’t said anything about nonnagitivity constraints, so I’ll assume there are none. The eigenvalues of the Hessian xy + xz + yz are -1, -1, 2. Therefore it is not convex (nor concave). Therefore xy + xz + yz < 1 is not a second order cone constraint, nor representable as such. It can not be entered into CVX.
Why do you “need” to write this as a second order cone constraint? BTW, professors have assigned many homework, take-home test, and thesis problems under false claims of convexity.