Phase Quantum Fisher Information Persists After Negativity Vanishes in Noisy CNOT Outputs

The authors map an input coherent qubit phase onto the coherence between |00> and |11> via CNOT, then apply post-gate noise. Negativity vanishes exactly when surviving coherence z equals the population penalty g, while phase QFI equals 4z^2/(a+b) and decays smoothly. This produces an exact region of state space where the output is separable but retains phase sensitivity. Four canonical channels trace trajectories through the same geometry and share the same residual QFI at the entanglement-death coordinate.

Asymmetric population transfer adds a third coordinate that alters negativity without changing QFI, confirming the two-coordinate description applies only inside a restricted subspace. A projective measurement attaining the QFI bound is identified, yet a direct single-qubit probe still outperforms the two-qubit protocol under equal exposure time. The work supplies reference benchmarks rather than a metrological claim.

The result challenges the usual assumption that entanglement sudden death marks the simultaneous loss of all useful quantum resources. It isolates phase information as a more robust quantity under the specific noise class considered, with direct implications for calibrating quantum gates in near-term processors where full entanglement may not be required for parameter estimation tasks.

Next steps include experimental tests in trapped-ion or superconducting architectures to measure the predicted residual QFI of 1/6 and to check whether additional realistic noise terms shrink the separable phase-sensitive region.