Solution
= Solution
The <spectral norm> of an operator $O$ is the induced <operator norm>
$$
\|O\|=\sup_{\|\psi\|=1}\|O\psi\|.
$$
Every <Pauli X gate> $X_i$ is <unitary operator>[unitary], so $\|X_i\|=1$. The <triangle inequality> for the norm therefore gives
$$
\boxed{\|J_X\|
\leq\sum_{i=1}^n\|X_i\|=n}.
$$
In fact equality holds, as the product of $+1$ <eigenvectors> of the $X_i$ has eigenvalue $n$ under $J_X$.