Repeated bell-basis projections as an entanglement-preserving protocol in noisy two-qubit registers

We analyze repeated rank-1 projections onto a single Bell state as an entanglement-preserving protocol for a noisy two-qubit register. The register interacts with a Markovian dissipative environment described by a Lindblad master equation, while each qubit also experiences classical frequency fluctuations with specified noise statistics. We focus on Ornstein–Uhlenbeck noise, using random telegraph noise and Poissonian jump noise as complementary models. Analytic asymptotic expressions are derived for the noise-averaged dynamics, and performance is evaluated using concurrence and a survival-gain metric comparing measurement-assisted evolution with free decay. We identify parameter regimes where repeated Bell-basis projections provide a robust advantage, as well as regimes where the benefit depends on noise statistics, revealing the role of non-Gaussian frequency fluctuations in entanglement protection.