Sequential measurement-device-independent entanglement detection by multiple observers
Chirag Srivastava, Shiladitya Mal, Aditi Sen, Ujjwal Sen
Abstract
Violation of a Bell inequality certifies that the underlying state must be entangled in a device-independent way, although there exist some entangled states which do not violate such an inequality. However, for every entangled state, it is possible to find a Hermitian operator called an entanglement witness that can detect entanglement through some local measurements in a device-dependent method, but implementation of wrong measurements may lead to fake detection of entanglement. To avoid such difficulties, measurement-device-independent entanglement witness (MDI-EW) based on a semiquantum nonlocal game was proposed, which is not only robust against wrong measurements but also against a specific kind of lossy detectors. We employ here a measurement-device-independent entanglement witness to detect entanglement in a scenario where half of an entangled pair is possessed by a single observer while the other half is with multiple observers performing unsharp measurements, sequentially, independently, and preserving entanglement as much as possible. Interestingly, we find that the numbers of successful observers who can detect entanglement, measurement-device-independently, both with equal and unequal sharpness parameters of the noisy measurements, are greater than that obtained with standard and Bell-inequality-based entanglement detection methods, reflecting its robustness. The entanglement contents of the sequentially shared states are also analyzed. Unlike other scenarios, our investigations also reveal that in this measurement-device-independent situation, states having entanglement in proximity to maximal remain entangled until there are two sequential observers, even if they measure sharply.