Quantifying Coherence-to-Entanglement Conversion Efficiency under Noisy Operations

• URL: http://arxiv.org/abs/2606.16916v1
• Date: Mon, 15 Jun 2026 16:23:27 GMT
• Title: Quantifying Coherence-to-Entanglement Conversion Efficiency under Noisy Operations
• Abstract summary: We investigate the noise-limited conversion of local quantum coherence into bipartite entanglement in a minimal two-qubit protocol.<n>We show that maximally coherent inputs not only maximize the entanglement generated by the CNOT protocol but also optimize its robustness against depolarizing noise.
• Score: 0.9051352746190449
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the noise-limited conversion of local quantum coherence into bipartite entanglement in a minimal two-qubit protocol comprising a coherent single-qubit input, an incoherent ancilla, an ideal CNOT operation, and subsequent environmental noise. Employing the $l_1$-norm of coherence and the entanglement negativity as resource quantifiers, we establish an exact closed-form correspondence between local single-qubit input coherence and the two-qubit entanglement generated in the noiseless limit, showing that the output negativity is precisely one half of the initial $l_1$-coherence. We then derive analytic expressions for the surviving entanglement and the associated coherence-to-entanglement conversion efficiency under two representative noise mechanisms: independent phase damping and global two-qubit depolarizing noise. The two channels exhibit qualitatively distinct degradation behavior. Phase damping induces a universal multiplicative suppression of the generated entanglement, yielding a coherence-independent conversion efficiency and no finite-noise entanglement sudden death. In contrast, global depolarization introduces an isotropic mixing contribution that shifts the partial-transpose spectrum, producing coherence-dependent degradation and a finite sudden-death threshold. We show that maximally coherent inputs not only maximize the entanglement generated by the CNOT protocol but also optimize its robustness against depolarizing noise. Direct density-matrix simulations validate the analytic results to numerical precision. These findings provide a compact analytic benchmark for assessing how different noise mechanisms constrain coherence-to-entanglement conversion in elementary quantum-information protocols and near-term quantum devices.

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