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Physical Review A

Collective multipartite Einstein-Podolsky-Rosen steering via cascaded four-wave mixing of rubidium atoms

Yang Liu, Yin Cai, Binshuo Luo, Jin Yan, Mengqi Niu, Feng Li, Yanpeng Zhang

Published Sep 7, 2021• 18 citations
Publisher

Abstract

Collective multipartite Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation shared among $n$ 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.

DOI
10.1103/physreva.104.033704

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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−1n\ensuremath{-}1n\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.
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.
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.
Collective multipartite Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation shared among N parties, where the EPR paradox of one party can only be realized by performing local measurements on all the remaining N-1 parties. We formalize the collective tripartite steering in terms of local hidden state model and give the steering inequalities that act as signatures and suggest how to optimize collective tripartite steering in specific optical schemes. The special entangled states with property of collective multipartite steering may have potential applications in ultra-secure multiuser communication networks where the issue of trust is critical.
Einstein–Podolsky–Rosen (EPR) steering is a key resource in the field of quantum information. It characterizes the ability of one party to exert remote influence on the state of another party through local operations. In this paper, we propose all-optical multipartite EPR steering swapping schemes with symmetric and asymmetric structures based on four-wave mixing (FWM) processes. Optical components are used to replace measurement devices or electronic feedforward devices in the traditional scheme, avoiding optic-electro and electro-optic conversions. The results show that both structures can verify the Gaussian-steered monogamous relationships, while the asymmetric structure produces stronger steering. Our schemes provide theoretical guidance for constructing all-optical broadband quantum networks.
Abstract Einstein–Podolsky–Rosen (EPR) steering for multipartite systems plays an important role in several quantum technologies and applications, e.g., quantum communication and quantum metrology. In this study, an energy‐level cascaded four‐wave mixing (EC‐FWM) process modulated by the dressing effect is proposed to generate three‐ and four‐mode EPR steering in the atomic medium of rubidium. The energy‐level simultaneously cascaded FWM and the energy‐level ordinally cascaded FWM are compared in three‐mode EPR steering, and monogamy relations for Gaussian steerability are also verified. Furthermore, multipartite EPR steerability is controlled by actively adjusting the dressing field. Different types of EPR steerability exhibit different modulation results when the dressing conditions of enhancement and suppression are satisfied. The proposed scheme exhibits advantages such as scalability, flexibility, and simplified experimental setup and can construct controllable large‐scale quantum networks.
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.