= Solution
\b[The state is separable.] The off-diagonal terms of the two <Bell state> projectors have opposite signs and cancel:
$$
\boxed{\frac12|\phi_+\rangle\langle\phi_+|+\frac12|\phi_-\rangle\langle\phi_-|
=\frac12|00\rangle\langle00|+\frac12|11\rangle\langle11|.}
$$
This is a <quantum state ensemble> of two <pure states> that are <product states>, with <probability> $1/2$ each, establishing a <separable quantum state>. Its correlations are classical; an ensemble decomposition into <entangled states> does not itself establish <quantum entanglement> of the <density matrix>.
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