Practical Advantage of Classical Communication in Entanglement Detection

Entanglement is the cornerstone of quantum communication, yet conventional detection relies solely on local measurements. In this work, we present a unified theoretical and experimental framework demonstrating that one-way local operations and classical communication (1-LOCC) can significantly outperform purely local measurements in detecting high-dimensional quantum entanglement. By casting the entanglement detection problem as a semidefinite program (SDP), we derive protocols that minimize false negatives at fixed false-positive rates. A variational generative machine-learning algorithm efficiently searches over high-dimensional parameter spaces, identifying states and measurement strategies that exhibit a clear 1-LOCC advantage. Experimentally, we realize a genuine event-ready protocol on a three-dimensional photonic entanglement source, employing fiber delays as short-lived quantum memories. We implement rapid, FPGA-based sampling of the optimized probabilistic instructions, allowing Bob's measurement settings to adapt to Alice's outcomes in real time. Our results validate the predicted 1-LOCC advantage in a realistic noisy setting and reduce the experimental trials needed to certify entanglement. These findings mark a step toward scalable, adaptive entanglement detection methods crucial for quantum networks and computing, paving the way for more efficient generation and verification of high-dimensional entangled states.