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New Journal of Physics

One to many one-way control in quadripartite asymmetric Einstein-Podolsky-Rosen steering

C Xiao, Xiaomao Cheng, Junwei Lv, Y. R. Shen, Yanxia Jiang, Long Cheng, Youbin Yu, Guangri Jin, Aixi Chen

Published Jan 1, 2024• 4 citations
Publisher

Abstract

Abstract Einstein–Podolsky–Rosen (EPR) steering is different from quantum entanglement because of its unique asymmetry. Multipartite asymmetric EPR steering can break through one-to-one monogamy steering and achieve one to many one-way steering. That is to say, the state of one part can steer the other rest parts simultaneously, while the other parts cannot steer this part. Here, a scheme is proposed to generate one to many one-way steering by optical parametric amplification cascaded with a sum-frequency generation process. One to many non-monogamy EPR steering, such as one to two and one to three one-way steering are demonstrated based on the criterion for asymmetric EPR steering. It is also find that different kinds of asymmetric EPR steering can be obtained by choosing different nonlinear parameters. This non-monogamous one to many quantum control has potential application in constructing quantum networks and realizing one-way quantum computing.

DOI
10.1088/1367-2630/ad1f0b

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Abstract Einstein–Podolsky–Rosen (EPR) steering is different from quantum entanglement because of its unique asymmetry. Multipartite asymmetric EPR steering can break through one-to-one monogamy steering and achieve one to many one-way steering. That is to say, the state of one part can steer the other rest parts simultaneously, while the other parts cannot steer this part. Here, a scheme is proposed to generate one to many one-way steering by optical parametric amplification cascaded with a sum-frequency generation process. One to many non-monogamy EPR steering, such as one to two and one to three one-way steering are demonstrated based on the criterion for asymmetric EPR steering. It is also find that different kinds of asymmetric EPR steering can be obtained by choosing different nonlinear parameters. This non-monogamous one to many quantum control has potential application in constructing quantum networks and realizing one-way quantum computing.
Einstein-Podolsky-Rosen (EPR) steering is a quantum effect based on quantum entanglement and it is the key resource for building quantum networks because of its useful properties. Based on the criterion for genuine multipartite EPR steering, the genuine quadripartite EPR steering is confirmed and it can be generated by a spontaneous parametric down-conversion cascaded process with two sum-frequency generations in an optical superlattice. This occurs either below the oscillation threshold and without oscillation threshold. The influence of the parameters of cascaded nonlinear process on the quadripartite EPR steering among signal, idler, and two sum-frequency beams are also discussed. Choosing appropriate nonlinear parameters can achieve good quadripartite quantum steering. This scheme of the generation of genuine quadripartite EPR steering has potential applications in quantum communication and computing.
Multipartite Einstein-Podolsky-Rosen (EPR) steering has been recognized as an essential resource for secure quantum communication tasks composed of several spatially separated parties who cannot be fully trusted. Nevertheless, this resource cannot be distributed arbitrarily over many parties; for instance, two independent players cannot simultaneously steer the third party by two-setting measurements. This feature is referred to as monogamy of steering, which ensures the security of quantum cryptographic protocols and is thus a very desired property to investigate for multipartite steering. Here, we propose symmetric and asymmetric structures of cascaded four-wave mixing of rubidium atoms to generate versatile quadripartite EPR steering and investigate four distinct types of monogamy relations of Gaussian steering. We find that the distribution constraint described by one of the monogamy relations can be lifted only for the quadripartite steering created by the symmetric setup. This result paves the way for a better understanding of the distribution rules of multipartite EPR steering and its potential applications for secure quantum communication.
Einstein-Podolsky-Rosen (EPR) steering, a category of quantum nonlocal correlations describing the ability of one observer to influence another party's state via local measurements, is different from both entanglement and Bell nonlocality by possessing an asymmetric property. For multipartite EPR steering, the monogamous situation, where two observers cannot simultaneously steer the state of the third party, has been investigated rigorously both in theory and experiment. In contrast to the monogamous situation, the shareability of EPR steering in reduced subsystems allows the state of one party to be steered by two or more observers and thus reveals more configurations of multipartite EPR steering. However, the experimental implementation of such a kind of shareability has still been absent until now. Here, in an optical experiment, we provide a proof-of-principle demonstration of the shareability of EPR steering without the constraint of monogamy in a three-qubit system. Moreover, based on the reduced bipartite EPR steering detection results, we verify the genuine three-qubit entanglement results. This work provides a complementary viewpoint for understanding multipartite EPR steering and has potential applications in many quantum information protocols, such as multipartite entanglement detection, quantum cryptography, and the construction of quantum networks.
Collective multipartite Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation shared among nnn parties, where the EPR paradox of one party can be realized only by performing local measurements on all the remaining $n\ensuremath{-}1$ parties. Here, we propose an efficient method to produce collective multipartite EPR steering via symmetrically and asymmetrically cascading parametric amplification processes, i.e., four-wave mixing (FWM) of rubidium atoms. The simplified collective-steering criterion is introduced using the Coffman-Kundu-Wootters monogamy relation. Moreover, by actively adjusting the parametric gains, the collective EPR steerability is optimized in our schemes. We find that the scale of collective steering can be extended by cascading more FWMs; in particular, introducing optical loss is useful for generating collective steering with more parties only in the asymmetry structure. Our results pave the way for the construction of quantum networks and provide a promising candidate for one-sided device-independent quantum cryptography among multiple users.
Asymmetric Einstein–Podolsky–Rosen (EPR) steering means the ability of one party to nonlocally “steer” the state in the other side through local measurements. The asymmetric property of EPR steering provides adequate security in one-sided device-independent secure quantum communication protocols. In this paper, we theoretically investigate the asymmetric EPR steering schemes between two subsystems of multipartite entangled states by an asymmetric modulation method. Two schemes, including tripartite entangled state to bipartite steering and quadripartite entangled state to tripartite steering, are investigated. By reconstructing the covariance matrix of continuous variable multipartite Gaussian states, we quantify the steerability of manipulating two different subsystems and demonstrate the EPR steering parameter versus various types of states’ parameters. Our work provides a reference for asymmetric quantum information processing and enriches resources for secure quantum networks.
Einstein-Podolsky-Rosen (EPR) steering has potential applications in quantum information processing. Here the genuine tripartite EPR steering is investigated in cascaded nonlinear process of spontaneous parametric down-conversion cascaded with a sum-frequency generation in an optical cavity for a wide range of the nonlinear parameters. The threshold properties of the cascaded nonlinear precess are also analyzed both below and without threshold regime, respectively. The genuine tripartite EPR steering is demonstrated based on the criteria for genuine multipartite EPR steering. Our scheme of the generation of genuine tripartite EPR steering can be used as a suggestion for the potential experiments and the applications in quantum communication and computation.