Notation

We use [n ] to denote {1,,n } for an integer n . To control the norm in the last line of (A.7), we note that The proof is along the lines of Theorem 1. This following lemma is useful for our proof. Applying Hermite decomposition (A.27) and taking expectation, we have Each summand in (A.28) is an n n matrix where We use the properties of Hermite polynomials [3][ 18.18.11]: 's form an orthogonal basis, equipped with the inner product This basis follows the physicist's convention of Hermite polynomial.