Unbounded Sharing of Nonlocality Using Projective Measurements

Abstract: It is a common perception that a sharp projective measurement in one side of the Bell experiment destroys the entanglement of the shared state, thereby preventing the demonstration of sequential sharing of nonlocality. In contrast, we introduce a local randomness-assisted projective measurement protocol, enabling the sharing of nonlocality by an arbitrary number of sequential observers (Bobs) with a single spatially separated party Alice. Subsequently, a crucial feature of the interplay between the degrees of incompatibility of observables of both parties is revealed, enabling the unbounded sharing of nonlocality. Our findings, not only offer a new paradigm for understanding the fundamental nature of incompatibility in demonstrating quantum nonlocality but also pave a new path for various information processing tasks based on local randomness-assisted projective measurement.