Detecting and protecting entanglement through nonlocality, variational entanglement witness, and nonlocal measurements

We present an advanced method to enhance the detection and protection of quantum entanglement, a key concept in quantum mechanics for computing, communication, and beyond. Entanglement, where particles remain connected over distance, can be indicated by nonlocality, measurable through the Clauser-Horne-Shimony-Holt (CHSH) inequality. While violating the inequality confirms entanglement, entanglement can still exist without such violations. To overcome this limitation, we use the CHSH violation as an entanglement measure and introduce a variational entanglement witness for more complete detection. Moreover, we propose a nonlocal measurement framework to measure the expectation values in both the CHSH inequality and variational entanglement witness. These nonlocal measurements exploit the intrinsic correlations between entangled particles, providing a more reliable approach for detecting and maintaining entanglement. This paper significantly contributes to the practical application of quantum technologies, where detecting and maintaining entanglement are essential.