= Singlet-triplet measurement causality obstruction
{title2=$\mathcal M(\rho)=P_s\rho P_s+(I-P_s)\rho(I-P_s)$}
The binary <Lüders rule> measurement of singlet versus triplet preserves the entire triplet subspace, but its nonselective channel permits signalling. Starting with $|00\rangle$, Bob retains $|0\rangle$. If Alice instead applies a local <Pauli X gate>, the input is $|10\rangle$ and the channel outputs the equal mixture of $|\Psi^+\rangle$ and $|\Psi^-\rangle$; Bob has <reduced density matrix> $I/2$. Thus no spacelike local implementation can realize this channel. A <Bell-state nondemolition measurement> has a finer triplet readout and a different nonselective channel, so this obstruction does not exclude it.
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