Analytic Benchmarks for Coherence-to-Entanglement Conversion Under Post-Gate Noise in CNOT-Based Protocols

Coherence-to-entanglement conversion transforms single-qubit superposition into a practical two-qubit resource, but noise limits this process in near-term quantum hardware. We derive closed-form benchmarks for a minimal CNOT primitive in which a coherent qubit and an incoherent ancilla generate entanglement before undergoing phase damping, global depolarizing, amplitude damping, or independent local depolarizing noise. Using the (Formula presented.) -norm of coherence and negativity, we prove the noiseless law (Formula presented.), valid for arbitrary mixed inputs, and obtain exact negativities, survival fractions, and entanglement-sudden-death thresholds. For all (Formula presented.) -state-preserving channels, a master relation shows that entanglement loss results from the competition between coherence suppression and partial-transpose spectral shifts. Phase damping yields (Formula presented.) without finite-noise sudden death; global depolarization gives coherence-dependent sudden death; amplitude damping adds an excited-population penalty and sudden death only for (Formula presented.); while local depolarization is most destructive at equal depolarizing strength. The initial survival slopes, (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.), act as compact noise fingerprints. Since concurrence satisfies (Formula presented.) for the generated states, all robustness rankings remain unchanged. Mapping channel parameters to (Formula presented.), (Formula presented.), and average gate fidelity connects the theory to hardware-level performance.