Bad Qubits — Learn Quantum by Doing

Multiple choice

For the singlet state

|\Psi^-\rangle

, Bob's reduced density matrix (tracing out Alice's qubit) is

\rho_B = (1/2)

times the identity. Why does this guarantee no-signalling?

$\rho_B$ forces Bob's outcome to always equal $+1$ regardless of his measurement axis
$\rho_B$ is a pure state that Alice can rotate to encode a message for Bob
$\rho_B$ is the maximally mixed state and does not depend on Alice's setting, so Bob's local statistics are unchanged no matter what Alice does
$\rho_B$ depends on Alice's measurement setting, allowing faster-than-light control of Bob's outcomes