Sharing of tripartite nonlocality by multiple observers measuring sequentially at one side

Abstract

Standard tripartite nonlocality and genuine tripartite nonlocality can be detected by the violations of Mermin inequality and Svetlichny inequality, respectively. Since tripartite quantum nonlocality has novel applications in quantum information and quantum computation, it is important to investigate whether more than three observers can share tripartite nonlocality, simultaneously. In the present study we answer this question in the affirmative. In particular, we consider a scenario where three spin-1 2 particles are spatially separated and shared between Alice, Bob and multiple Charlies. Alice performs measurements on the first particle; Bob performs measurements on the second particle and multiple Charlies perform measurements on the third particle sequentially. In this scenario we investigate how many Charlies can simultaneously demonstrate standard tripartite nonlocality and genuine tripartite nonlocality with single Alice and single Bob. The interesting result revealed by the present study is that at most six Charlies can simultaneously demonstrate standard tripartite nonlocality with single Alice and single Bob. On the other hand, at most two Charlies can simultaneously demonstrate genuine tripartite nonlocality with single Alice and single Bob. Hence, the present study shows that standard tripartite nonlocality can be simultaneously shared by larger number of Charlies compared to genuine tripartite nonlocality in the aforementioned scenario, which implies that standard tripartite nonlocality is more effective than genuine tripartite nonlocality in the context of simultaneous sharing by multiple observers.

Unbounded sequence of observers exhibiting Einstein-Podolsky-Rosen steering

“…Let us comment on that point. Previously, in the non-anonymous case, the same scaling was obtained for all measurements and CSMUB (see Eqs (18) and (26)), as the proofs relied only on the fact that p iso steer tends to 0 when d goes to infinity. In the scenario we are now considering, as fewer assumptions are needed, the scaling depends on the precise behavior of p iso steer (d).…”

“…This motivated further work exploring the potential of these ideas for randomness generation [13] and their classical communication cost [14], and led to experimental demonstrations [15,16]. More recently, these ideas were extended to other types of quantum correlations [17][18][19]. Specifically, Ref.…”

Arbitrarily Many Independent Observers can Share the Nonlocality of a Single Maximally Entangled Qubit Pair

“…Since the presence of non-locality implies the possibility of steering and the presence of entanglement, our work shows that it is also possible to achieve both of these with arbitrarily many independent Bobs using only a single pair of entangled qubits. This goes against some of the results in [18,22,23], and suggests that it is worth rethinking others that study the space of such correlations [24] or look at other Bell in-equalities [25] or more parties [26,27] after removing the assumption that both measurements used by each party have the same sharpness.…”

Sharing quantum steering among multiple Alices and Bobs via a two-qubit Werner state

“…Recently, a surprising result was reported by Silva et al that the number of observers sharing non-locality can be increased if the sequential weak (unsharp) measurement was employed, where the non-signaling condition is dropped [27]. Their result later is confirmed by theoretical [28][29][30] as well as experimental works [31,32], and the sequential unsharp measurement strategy has been extended to study other types of quantum correlation [33][34][35]. It has shown that the maximum number of Alices who can simultaneously share steering with a single Bob can also beat the steering monogamy limits [36][37][38].…”