Facets of bipartite nonlocality sharing by multiple observers via sequential measurements

Recently, it has been shown that at most two observers (Bobs) can sequentially demonstrate bipartite nonlocality with a spatially separated single observer (Alice) invoking a scenario where an entangled system of two spin-$\frac{1}{2}$ particles are shared between a single Alice in one wing and several Bobs on the other wing, who act sequentially and independently of each other [Phys. Rev. Lett. 114, 250401 (2015)]. This has been probed through the quantum violations of CHSH inequality, i.e., when each observer performs two dichotomic measurements. In the present study we investigate how many Bobs can sequentially demonstrate bipartite nonlocality with a single Alice in the above scenario when the number of measurement settings per observer is increased. It is shown that at most two Bobs can exhibit bipartite nonlocality with a single Alice using local realist inequalities with three as well as four dichotomic measurements per observer. We then conjecture that the above feature remains unchanged contingent upon using local realist inequalities with $n$ dichotomic measurements per observer, where $n$ is arbitrary. We further present the robustness of bipartite nonlocality sharing in the above scenario against the entanglement and mixedness of the shared state.

Figure 1

Solid black line indicates spatial separation and dashed black line indicates time separation. Alice performs measurements on one particle and multiple Bobs (${\mathrm{Bob}}^1$, ${\mathrm{Bob}}^2$, ${\mathrm{Bob}}^3$,..., ${\mathrm{Bob}}^n$) perform measurements on the other particle sequentially.