Sharing Quantum Steering via Standard Projective Measurements

Abstract: We propose a scheme for the sharing of quantum steering among three observers, Alice, Bob, and Charlie using standard projective measurements. We show that in the unilateral sequential scenario, Alice can steer Bob's and Charlie's states and conversely, Bob and Charlie can steer Alice's state. Unlike the quantum steering sharing achieved through weak measurements, we use the standard projective measurements to enable quantum steering sharing. Quantum steering is demonstrated by the violations of the linear steering inequality among different observer combinations. We find that Alice can simultaneously steer both Bob's and Charlie's states, and Bob and Charlie can simultaneously steer Alice's state, regardless of whether they are in maximally entangled states or partially entangled states. The maximum double violation of the linear steering inequalities obtained from partially entangled states can be greater in some cases than that obtained from maximally entangled states when randomly combining the case of two projective measurements and the case of two identity measurements. Additionally, we verify hybrid quantum correlation sharing through the double violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality and the linear steering inequality. Our results provide a new perspective for the study of quantum steering and may lead to applications in quantum random access code, randomness certification, and self-testing process.