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Optics Express

Witnessing multi-observer steering on both sides simultaneously via weak measurements

Tong-Jun Liu, Kun Liu, Wei Fang, Jian Li, Qin Wang

Published Oct 13, 2022• 4 citations
Publisher

Abstract

The quantum steering as an intermediate form of quantum correlations, has various peculiarities differing from the Bell nonlocality and the quantum entanglement. In a specific scenario, each side of the observer shares one of the two entangled qubits, steering can be witnessed simultaneously between any two observers from different sides by performing weak or projective measurements successively, with independently chosen and unbiased inputs. Here, we demonstrate this steering scenario experimentally to simultaneously witness quartic Einstein-Podolsky-Rosen steerings of two successive observers between each side with the entangled pair with a state fidelity of 97.6% compared with a maximally-entangled one.

DOI
10.1364/oe.470229

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The quantum steering as an intermediate form of quantum correlations, has various peculiarities differing from the Bell nonlocality and the quantum entanglement. In a specific scenario, each side of the observer shares one of the two entangled qubits, steering can be witnessed simultaneously between any two observers from different sides by performing weak or projective measurements successively, with independently chosen and unbiased inputs. Here, we demonstrate this steering scenario experimentally to simultaneously witness quartic Einstein-Podolsky-Rosen steerings of two successive observers between each side with the entangled pair with a state fidelity of 97.6% compared with a maximally-entangled one.
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.
Quantum correlation is a fundamental property that distinguishes quantum systems from classical ones, and is also a fragile resource under projective measurements. Recently, it has been shown that a subsystem in entangled pairs can share nonlocalities with multiple observers in sequence. Here we present a new steering scenario where both subsystems are accessible by multiple observers. Simulation results show that the two qubits in a singlet state can be simultaneously steered separately by two sequential observers.
The Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum nonlocality between entanglement and Bell nonlocality, which plays an important role in quantum information processing tasks. In the past few years, the investigations concerning the EPR steering have been demonstrated in a series of experiments. However, these studies rely on the relevant steering inequalities and the choices of measurement settings. Here, we experimentally verify the EPR steering via entanglement detection without using any steering inequality and measurement setting. By constructing two new states from a two-qubit state, we observe the EPR steering by detecting the entanglement of these new states. The results show that the entanglement of the newly constructed states can be regarded as an unusual kind of steering witness for these states. Compared to the results of Xiao et al. [Phys. Rev. Lett. 118, 140404 (2017)], we find that the ability to detect the EPR steering in our scenario is stronger than that of two-setting projective measurements, which can observe more steerable states. Hence, our demonstrations can deepen the understanding of the connection between the EPR steering and entanglement.
Abstract Recently, both global and local classical randomness-assisted projective measurement protocols have been employed to share Bell nonlocality of an entangled state among multiple sequential parties. Unlike Bell nonlocality, Einstein–Podolsky–Rosen (EPR) steering exhibits distinct asymmetric characteristics and serves as the necessary quantum resource for one-sided device-independent quantum information tasks. In this work, we propose a projective measurement protocol and investigate the shareability of EPR steering with steering radius criterion theoretically and experimentally. Our results reveal that arbitrarily many independent parties can share one-way steerability using projective measurements, even when no shared randomness is available. Furthermore, by leveraging only local randomness, asymmetric two-way steerability can also be shared. Our work not only deepens the understanding of the role of projective measurements in sharing quantum correlations but also opens up a new avenue for reutilizing asymmetric quantum correlations.
Protocols for testing or exploiting quantum correlations---such as entanglement, Bell nonlocality, and Einstein-Podolsky-Rosen steering---generally assume a common reference frame between two parties. Establishing such a frame is resource intensive and can be technically demanding for distant parties. While Bell nonlocality can be demonstrated with high probability for a large class of two-qubit entangled states when the parties have one or no shared reference direction, the degree of observed nonlocality is measurement-orientation dependent and can be arbitrarily small. In contrast, we theoretically prove that steering can be demonstrated with 100100%100 probability for a larger class of states, in a rotationally invariant manner, and experimentally demonstrate rotationally invariant steering in a variety of cases. We also show, by comparing with the steering inequality of Cavalcanti et al. [J. Opt. Soc. Am. B 32, A74 (2015)], that the steering inequality we derive is the optimal rotationally invariant one for the case of two settings per side and maximally mixed local qubit states.
Einstein-Podolsky-Rosen (EPR) steering describes the ability of one observer to nonlocally "steer" the other observer's state through local measurements. EPR steering exhibits a unique asymmetric property; i.e., the steerability can differ between observers, which can lead to one-way EPR steering in which only one observer obtains steerability in the steering process. This property is inherently different from the symmetric concepts of entanglement and Bell nonlocality, and it has attracted increasing interest. Here, we experimentally demonstrate asymmetric EPR steering for a class of two-qubit states in the case of two measurement settings. We propose a practical method to quantify the steerability. We then provide a necessary and sufficient condition for EPR steering and clearly demonstrate one-way EPR steering. Our work provides new insight into the fundamental asymmetry of quantum nonlocality and has potential applications in asymmetric quantum information processing.