Variance of the sum of independent quantum computing errors

The sum of quantum computing errors is the key element both for the estimation and control of errors in quantum computing and for its statistical study. In this article we analyze the sum of two independent quantum computing errors, $X_1$ and $X_2$, and we obtain the formula of the variance of the sum of these errors: $$ V(X_1+X_2)=V(X_1)+V(X_2)-\frac{V(X_1)V(X_2)}{2}. $$ We conjecture that this result holds true for general quantum computing errors and we prove the formula for independent isotropic quantum computing errors.