Diagonal absolute-sum bound for the trace norm
= Diagonal absolute-sum bound for the trace norm
{title2=$\sum_i|\langle\psi_i|X|\psi_i\rangle|\leq\|X\|_1$}
For any <orthonormal basis> and <Hermitian operator>, $\sum_i|\langle\psi_i|X|\psi_i\rangle|\leq\|X\|_1$. In the <trace-norm variational principle for Hermitian operators>, choose the diagonal $T$ whose entries are the signs of these diagonal entries. This bounds the total distinguishability visible in one fixed measurement basis.