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Physical Review A

Monogamy relations within quadripartite Einstein-Podolsky-Rosen steering based on cascaded four-wave mixing processes

Yu Xiang, Yang Liu, Yin Cai, Feng Li, Yanpeng Zhang, Qiongyi He

Published May 15, 2020• 32 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.101.053834

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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.
Multipartite Einstein-Podolsky-Rosen (EPR) steering is an essential resource for secure one-sided device-independent quantum secret sharing. Here, we analyze the EPR steering properties exhibited in three-mode Gaussian states created by four-wave mixing (FWM) in Rubidium atoms combined with a linear beamsplitter and a nonlinear beamsplitter (second FWM), respectively. By quantifying Gaussian steerability based on a measure determined by the covariance matrix of the produced states, we compare the performance of two schemes to achieve one-way, collective, and genuine tripartite steering, as well as the monogamy constraints for distributing steering among three parties. We show that the scheme with nonlinear beamsplitter is feasible to create stronger bipartite steering and genuine tripartite steering and has more flexibility to manipulate the monogamy relation through the cooperation of the two cascaded FWM processes.
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.
Understanding how quantum resources can be quantified and distributed over many parties has profound applications in quantum communication. As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. By reconstructing the covariance matrix of a continuous variable four-mode square Gaussian cluster state subject to asymmetric loss, we quantify the amount of bipartite steering with a variable number of modes per party, and verify recently introduced monogamy relations for Gaussian steerability, which establish quantitative constraints on the security of information shared among different parties. We observe a very rich structure for the steering distribution, and demonstrate one-way EPR steering of the cluster state under Gaussian measurements, as well as one-to-multimode steering. Our experiment paves the way for exploiting EPR steering in Gaussian cluster states as a valuable resource for multiparty quantum information tasks.
In a quantum communication network, multipartite Einstein–Podolsky–Rosen (EPR) steering has become an important resource and has attracted much attention because of its important role in quantum secret sharing and quantum secure communication. In this paper, we investigate the multipartite EPR steering characteristics of symmetric and asymmetric structures based on four-wave mixing (FWM) processes. Multipartite quantum steering, among the four output light fields produced by two structures, is theoretically analyzed. We find that both symmetric and asymmetric structures can verify Gaussian steered monogamous relationships, but the asymmetric structure produces stronger steering and has more flexibility to manipulate monogamous relationships. The results presented here may find potential applications in secure quantum information manipulation processes.
Multipartite Einstein-Podolsky-Rosen (EPR) steering has been widely studied, for realizing safer quantum communication. The steering properties of six spatially separated beams from the four-wave-mixing process with a spatially structured pump are investigated. Behaviors of all (1+i)/(i+1)-mode (i=1,2,3) steerings are understandable, if the role of the corresponding relative interaction strengths are taken into account. Moreover, stronger collective multipartite steerings including five modes can be obtained in our scheme, which has potential applications in ultra-secure multiuser quantum networks when the issue of trust is critical. By further discussing about all monogamy relations, it is noticed that the type-IV monogamy relations, which are naturally included in our model, are conditionally satisfied. Matrix representation is used to express the steerings for the first time, which is very useful to understand the monogamy relations intuitively. Different steering properties obtained in this compact phase-insensitive scheme have potential applications for different kinds of quantum communication tasks.
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.