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arXiv:2405.08588 · Physical Review A

Sharing quantum steering via standard projective measurements

Shufen Dong, Zinuo Cai, Chunfeng Wu, Changliang Ren

Published Jul 1, 2024• 5 citations
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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 may not be greater in some cases than that obtained from maximally entangled states. 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 an alternative perspective for studying quantum steering and hybrid quantum correlation and may lead to applications in quantum random access code, randomness certification, and self-testing processes.

DOI
10.1103/physreva.110.012203

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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 may not be greater in some cases than that obtained from maximally entangled states. 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 an alternative perspective for studying quantum steering and hybrid quantum correlation and may lead to applications in quantum random access code, randomness certification, and self-testing processes.
We aim to explore the scenario that a single Alice steers multiple Bobs by using weak measurements. The multiple violations of two different Einstein-Podolsky-Rosen steering inequalities were discussed. Based on unbiased inputs, a single Alice can steer two Bobs when the double violation of the Clauser-Horne-Shimony-Holt-like inequality is realized. Meanwhile, three Bobs can be steered by a single Alice when the triple violation of the three-settings linear steering inequality is observed. More importantly, we theoretically inferred the analytical formula of the maximal violation for the corresponding inequality, which applied an arbitrary two-qubit state.
Abstract In the standard Bell experiment, two parties perform local projective measurements on a shared pair of entangled qubits to generate nonlocal correlations. However, these measurements completely destroy the entanglement, rendering the post-measurement state unable for subsequent use. For a long time, it was believed that only unsharp measurements can be used to share quantum correlations. Remarkably, recent research has shown that classical randomness assisted projective measurements are sufficient for sharing nonlocality (Steffinlongo and Tavakoli 2022 Phys. Rev. Lett. 129 230402). Here, by stochastically combining no more than two different projective measurement strategies, we report an experimental observation of double Clauser–Horne–Shimony–Holt inequality violations with two measurements in a sequence made on each pair of maximally and partially entangled polarization photons. Our results reveal that the double violation achieved by partially entangled states can be 11 standard deviations larger than that achieved by maximally entangled ones. Our scheme eliminates the requirement for entanglement assistance in previous unsharp-measurement-based sharing schemes, making it experimentally easier. Our work provides possibilities for sharing other types of quantum correlations in various physical systems with projective measurements.
Quantum mechanics puts a restriction on the number of observers who can simultaneously steer another observer's system, known as the monogamy of steering. In this work, we find the limit of the number of observers (Bobs) who can steer another party's (Alice's) system, invoking a scenario where half of an entangled pair is shared between a single Alice in one wing and several Bobs on the other wing, who act sequentially and independently of each other. When all the observers measure two dichotomic observables, we find that two Bobs can steer Alice's system, going beyond the monogamy restriction. We further show that three Bobs can steer Alice's system, considering a three-settings linear steering inequality, and then conjecture that, at most, nnn Bobs can demonstrate steering of Alice's system when steering is probed through an nnn-settings linear steering inequality.
Quantum correlation is a fundamental resource for various quantum information tasks. It is thus of importance to share the correlation to utilize it for many parties, but sharing quantum correlation among multiple parties is strictly restricted by the well-known monogamy relations. Nonetheless, this restriction can be relaxed when weak measurements are employed. Here, we experimentally demonstrate multiple-observer quantum steering by exploiting sequential weak measurements. Specifically, we observe simultaneous triple violations of the quantum steering inequality among four observers for a bipartite entangled system. Our results not only provide fundamental insights into the relation between quantum steering and measurement disturbance, but also suggest that quantum steering might be repeatably exploited to find applications to, for example, unbounded randomness certification and sharing secret keys among multiple parties simultaneously.
Nonlocality and quantum measurement are two fundamental topics in quantum theory and their interplay attracts intensive focuses since the discovery of Bell theorem. Recently, nonlocality sharing among multiple observers with one entangled pair has been predicted and experimentally observed by generalized quantum measurement---weak measurement. However, only the one-sided sequential case, i.e., one Alice and multiple Bobs, is widely discussed and little is known about the two-sided case. Here, we theoretically and experimentally explore the nonlocality sharing in the two-sided sequential measurements case in which one entangled pair is distributed to multiple Alices and Bobs. We experimentally observed double Einstein-Podolsky-Rosen (EPR) steering among four observers in a photonic system. In the case that all observers adopt the same measurement strength of the weak measurement, it is observed that double EPR steering can be demonstrated simultaneously. The results not only deepen our understanding of relation between sequential measurements and nonlocality but also may find important applications in many quantum information tasks, such as randomness certification.
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.