Partial Trace — Tracing Away One Qubit Kills All Coherence

The Bell state is perfectly pure. Trace out qubit B and what remains is maximally mixed. All quantum correlation was between the parts, not within one.

Joint ρ_AB
Reduced ρ_A = Tr_B(ρ_AB)
Measures
Purity Tr(ρ²)
Entropy S (bits)
Off-diagonals of ρ_A are always zero here — entanglement has no local signature. The full ρ_AB has off-diagonals; they are traced away.
θ = 45.0° 0° = product state  ·  45° = Bell |Φ+⟩