Abstract While previous studies on sequential quantum sharing rely on either sharp measurements for ‘non-local’ entangled states or weak measurements for ‘local’ entangled states, we bridge this gap by investigating ‘local’ entangled states under a robust projective measurement framework. We demonstrate that probabilistic projective measurements with fixed probability can enable entanglement sharing for certain ‘local’ entangled states. Furthermore, we show that by probabilistic combination of certain different projective measurement strategies, the entanglement sharing can be expanded even under strict probability constraints. Subsequently, we prove that under projective measurements with deterministic probabilities, the maximum number of observers capable of sharing entanglement for ‘local’ entangled states is explicitly derived in terms of the entanglement of the initial state. Finally, the relationship among the sharing capacity, the initial state’s entanglement and the measurement strength of projective measurements is analytically presented.
Abstract While previous studies on sequential quantum sharing rely on either sharp measurements for ‘non-local’ entangled states or weak measurements for ‘local’ entangled states, we bridge this gap by investigating ‘local’ entangled states under a robust projective measurement framework. We demonstrate that probabilistic projective measurements with fixed probability can enable entanglement sharing for certain ‘local’ entangled states. Furthermore, we show that by probabilistic combination of certain different projective measurement strategies, the entanglement sharing can be expanded even under strict probability constraints. Subsequently, we prove that under projective measurements with deterministic probabilities, the maximum number of observers capable of sharing entanglement for ‘local’ entangled states is explicitly derived in terms of the entanglement of the initial state. Finally, the relationship among the sharing capacity, the initial state’s entanglement and the measurement strength of projective measurements is analytically presented.
Recently, Sasmal et al. [Phys. Rev. Lett. 133, 170201 (2024)] introduced probabilistic projective measurements (PPMs) for sequential sharing of nonlocality. Here we develop a general framework for sequentially witnessing quantum correlations, including bipartite and genuine multipartite entanglement, via PPMs. We show that a class of positive-operator-valued measures admits a unified PPM realization and present an explicit formula linking the initial state, intermediate channels, and witness operators, providing both computational efficiency and structural insight. Using this framework, we demonstrate unbounded sequential entanglement sharing for pure and certain mixed states, as well as detection of genuine multipartite entanglement in Greenberger-Horne-Zeilinger-type states. Our results highlight the nontrivial role of PPMs in sequential entanglement witnessing and address generalized multipartite sharing, as discussed in a recent review article [Phys. Rep. 1098, 1 (2025)].
We investigate entanglement sharing in a two-qubit sequential measurement scenario using three complementary classical correlation metrics: mutual information (I), sum of conditional probabilities (S), and the Pearson correlation coefficient (C). By investigating both weak measurement and probabilistic projective measurement (PPM) strategies in unilateral and bilateral scenarios, the phenomenon of entanglement sharing is conclusively certified when multiple pairs of classical correlation metrics simultaneously exceed their thresholds. Our investigation reveals that weak measurement strategies are more favorable than PPM for exhibiting entanglement sharing, regardless of the scenario. Furthermore, the mutual information criterion fails to characterize entanglement sharing in the bilateral scenario. While, the Pearson correlation criterion (C) is proven to be the most robust across all strategies and scenarios. These findings unveil a critical trade-off between measurement disturbance and complementary correlation recovery, which is essential for quantum resource reuse problems.
The prevailing consensus is that the sequential sharing of nonlocality in a Bell experiment requires generalized unsharp measurements, given that a sharp measurement inevitably destroys the entanglement of the shared state. In contrast, a recent work [A. Steffinlongo and A. Tavakoli, Projective measurements are sufficient for recycling nonlocality, Phys. Rev. Lett. 129, 230402 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.230402] demonstrated the sharing of nonlocality up to two sequential observers by employing projective measurement aided with local randomness. Here, we introduce a form of local randomness-assisted qubit projective measurement protocol that enables the sharing of nonlocality by an arbitrary number of sequential observers (Bobs) with a single spatially separated observer (Alice). We achieve this by inspecting the diversity involved in implementing generalized measurements that harness nonlocality by preserving a sufficient amount of entanglement of the shared two-qubit entangled state. Furthermore, we highlight the crucial interplay between the degrees of measurement incompatibility of Alice and Bob in demonstrating the unbounded sharing of nonlocality.
Abstract Bell nonlocality is a valuable resource in quantum information processing tasks. Scientists are interested in whether a single entangled state can generate a long sequence of nonlocal correlations. Previous work has accomplished sequential tripartite nonlocality sharing through unsharp measurements. In this paper, we investigate the sharing of tripartite nonlocality using only projective measurements and sharing classical randomness. For the generalized GHZ state, we have demonstrated that using unbiased measurement choices, two Charlies can share the standard tripartite nonlocality with a single Alice and a single Bob, while at most one Charlie can share the genuine tripartite nonlocality with a single Alice and a single Bob. However, with biased measurement choices, the number of Charlies sharing the genuine tripartite nonlocality can be increased to two. Nonetheless, we find that using biased measurements does not increase the number of sequential observers sharing the standard tripartite nonlocality. Moreover, we provide the feasible range of double violation for the parameters of the measurement combination probability with respect to the state.
Sequential sharing of quantum nonlocality (SSQN) is crucial for device-independent tasks in quantum information processing, wherein relaying the post-measurement qubit through a local quantum channel to a subsequent observer constitutes an essential operational step. Here we present a theoretical analysis of noise robustness of sequential sharing for bipartite Bell and tripartite Mermin nonlocality under the influence of local phase-flip, bit-flip, and depolarizing quantum channels. It is proved that arbitrarily many independent observers can sequentially share the quantum nonlocality of Bell, Greenberger-Horne-Zeilinger, and W states via respective noise-immune channels, whereas such unbound feature of SSQN is lost under other local noisy quantum channels. Furthermore, we demonstrate that the noise-immune channel enabling unbounded SSQN can be switched by employing our newly designed measurement strategies assisted by local unitary operations on the initial entangled states. Moreover, as illustrative examples of noise robustness, we propose two concrete schemes for sharing Bell and Mermin nonlocality with two sequential local observers on one side subject to local noisy channels. Our work establishes a practical framework for realizing the SSQN under noisy quantum channels, and reveals the connection between noise robustness and measurement strategies.
Sequential measurements present a novel framework for constructing large-scale quantum networks, particularly in quantum correlation sharing. In this paper, we design projective measurements and combination strategies to achieve nonlocality sharing in star-shaped networks by leveraging shared classical randomness. This network consists of n branches, each containing one or two sequential observers. By investigating two-sided nonlocality sharing within a 2-local network, we identify the optimal projective measurement combination strategy based on the double violation of the 2-locality inequality. Utilizing this optimal strategy, we demonstrate that four inequalities can be violated simultaneously in the 2-local scenario. Furthermore, in an n-local scenario involving m ($1\ensuremath{\le}m\ensuremath{\le}n$) branches with two sequential observers, our optimal strategy shows that non-n-locality sharing among all observers can be achieved through the simultaneous violation of 2mn-locality inequality. Our findings provide a distinctive perspective on quantum correlation sharing in networks.