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Journal of the Optical Society of America B

Einstein–Podolsky–Rosen steering based on hexapartite coherent feedback control in four-wave mixing with a spatially structured pump

Shuqin Zhai, Jinrui Zhou, Kui Liu

Published Apr 7, 2026• 1 citation
Publisher

Abstract

Quantum steering, as a fundamental resource in quantum information science, is a key resource for secure quantum communication networks. Coherent feedback control (CFC) has been widely used to enhance squeezing. In this paper, we utilize a variable beam splitter (VBS) with a reflectivity of k as the feedback controller to build a coherent feedback control system in four-wave mixing (FWM) processes with a spatially structured pump (SSP). We investigate the influence of feedback strength and interaction intensity on quantum steering across different modes under specific phase delay conditions. The results show that the coherent feedback control system can flexibly control quantum steering. By adjusting the parameters, we can achieve various quantum steering types, especially collective multipartite steering and genuine multipartite steering. It has significant practical application value for secure quantum information processing and offers a theoretical reference for the construction of large-scale, secure quantum networks.

DOI
10.1364/josab.591478

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Quantum steering, as a fundamental resource in quantum information science, is a key resource for secure quantum communication networks. Coherent feedback control (CFC) has been widely used to enhance squeezing. In this paper, we utilize a variable beam splitter (VBS) with a reflectivity of k as the feedback controller to build a coherent feedback control system in four-wave mixing (FWM) processes with a spatially structured pump (SSP). We investigate the influence of feedback strength and interaction intensity on quantum steering across different modes under specific phase delay conditions. The results show that the coherent feedback control system can flexibly control quantum steering. By adjusting the parameters, we can achieve various quantum steering types, especially collective multipartite steering and genuine multipartite steering. It has significant practical application value for secure quantum information processing and offers a theoretical reference for the construction of large-scale, secure quantum networks.
Quantum coherent feedback control (CFC) has been widely applied to prepare and manipulate nonclassical beams. In this paper, we utilize an optical beam splitter with tunable reflectivity kkk as a feedback controller and theoretically construct a CFC system based on four-wave mixing (FWM) processes with a spatially structured pump. After considering absorption loss in the atoms, beam propagation loss in the feedback loop, and detection loss in the detectors, we derive an input-output relationship and theoretically study the manipulation of feedback strength, gain of the FWM processes, and phase to the degree of hexapartite quantum correlation of the system. We find that the relative intensity-difference squeezing degree of all the six output fields from this system is enhanced within a certain range of feedback ratio and phase. Furthermore, there exists an optimal feedback ratio and phase to maximize the intensity-difference squeezing. In addition, we also study the entanglement properties of this CFC system by the positivity under the partial transposition criterion and find that the feedback ratio and phase can tailor the entanglement structure of the hexapartite state. The proposed CFC scheme has realized quantum correlation enhancement and entanglement manipulation, which can be expanded to a large-scale quantum network for more practical applications in quantum information processing.
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.
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.
Coherent feedback control (CFC) has been proven to be a promising approach for manipulating nonclassical light beams. In this paper, a CFC scheme based on the spatial multiplexing cascaded four-wave mixing (FWM) process is proposed, employing a beam splitter as a feedback controller. Considering the absorption loss of the atomic vapor and the transmission loss of the feedback loop, the input–output relationship of the CFC system is derived. Based on this, the quadripartite quantum correlation of the CFC system versus the feedback strength, phase delay of the feedback loop, gain of the FWM process, and the losses is studied. It is found that the quadripartite quantum correlation can be enhanced within a certain range of feedback ratio and phase. Furthermore, there always exists an optimal feedback ratio to maximize the correlation. In addition, the bipartite correlation present in the multiple quantum correlated beams is also investigated. The numerical calculation based on feasible physical parameters of realistic systems provides direct references for the experimental design, which may find applications in quantum communication and quantum metrology.
Abstract Multipartite quantum steering has important applications in secure quantum communication networks. In this work, three different energy-level cascaded four-wave mixing (FWM) processes are proposed to generate quadripartite quantum steering. The covariance matrix among different modes combination is constructed. The properties of quantum steering of the three cascaded models were studied. The results show that all three model structures can achieve various types of quantum steering, and the steerability varies with the amplitude gain of the FWM processes. The results provide a theoretical basis for the experimental generation of multipartite quantum steering and a significant reference for secure quantum communication.
Einstein–Podolsky–Rosen (EPR) steering is a type of directional quantum correlation that holds immense significance and broad applications in quantum information processing. While EPR steering has been achieved across various physical systems, research into its implementation in non-Hermitian systems remains in its early stages. In this study, we delve into the realm of non-Hermitian control of EPR steering by leveraging atomic coherence-controlled energy-level cascaded four-wave mixing (ELC-FWM) processes. We derive analytical expressions for the generation of EPR steering within such non-Hermitian nonlinear systems, demonstrating that exceptional points (EPs) and multimode EPR steering can be realized through introducing dressing-control fields. Furthermore, we illustrate that nonlinear coherent channels and the associated steerability distribution of the output modes can be tailored during the EPR steering generation process, which is directly linked to the eigenvalues of non-Hermitian processes. Additionally, we analyze the impact of loss effects on generated multimode EPR steering. Our findings suggest that non-Hermitian control offers a promising all-optical approach for constructing practical quantum networks.