Solution
= Solution
The <Quantum no-signalling>[no-signalling theorem] states that any trace-preserving quantum operation performed locally by Bob leaves Alice's reduced density matrix unchanged when Bob's outcome is not communicated:
$$
\operatorname{Tr}_B[(I\otimes\mathcal E_B)(\rho_{AB})]
=\operatorname{Tr}_B\rho_{AB}.
$$
\b[Thus Bob's choice cannot change the statistics of any measurement made by Alice.]