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arXiv:2403.16346 · International Journal of Quantum Information

Manipulating the direction of one-way steering in an optomechanical ring cavity

Jamal El Qars, Benachir Boukhris, Ahmed Tirbiyine, Abdelaziz Labrag

Published Nov 13, 2023• 2 citations
arXivHTMLPDF

Abstract

Quantum steering refers to the apparent possibility of exploiting nonseparable quantum correlations to remotely influence the quantum state of an observer via local measurements. Different from entanglement and Bell nonlocality, quantum steering exhibits an inherent asymmetric property, which makes it relevant for many asymmetric quantum information processing tasks. Here, we study Gaussian quantum steering between two mechanical modes in an optomechanical ring cavity. Using experimentally feasible parameters, we show that the state of the two considered modes can exhibit two-way steering and even one-way steering. Instead of using unbalanced losses or noises, we propose a simple practical way to control the direction of one-way steering. A comparative study between the steering and entanglement of the studied modes shows that both steering and entanglement undergo a sudden death-like behavior. In particular, steering is found more fragile against thermal noise remaining constantly upper-bounded by entanglement. The proposed scheme may be meaningful for one-sided device-independent quantum key distribution, where the security of such protocol depends fundamentally on the direction of steering.

DOI
10.1142/s0219749923500430

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Abstract We theoretically investigate the emergence and asymmetry of Gaussian quantum steering and Rényi-2 entanglement in the radiation field of a nondegenerate three-level laser system. The gain medium consists of atoms initially prepared in a coherent superposition of the upper and lower states, interacting with two quantized cavity modes coupled to a common thermal reservoir. Using the steady-state solution of the master equation and the covariance matrix formalism, we compute the Gaussian steerability in both directions and compare it to the Gaussian Rényi-2 entanglement. Our analysis reveals that, under a wide range of parameters—including gain strength, population inversion, and thermal phonon number—the system exhibits generic one-way steering from mode A to mode B , with the reverse direction being inaccessible. This asymmetry is shown to originate from the photon number imbalance between the two modes. We further demonstrate that thermal noise degrades quantum correlations, with steering being more fragile than entanglement. These results provide theoretical support for the implementation of asymmetric quantum information protocols in cavity-based platforms and could be tested with current experimental technologies.

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Asymmetric Two-Way Gaussian Quantum Steering in Coupled Lossy Waveguides

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Quantum steering is an important type of quantum correlation with potential applications in one-sided device-independent (1SDI) quantum information protocols. In this contribution, we explore the time-dependent dynamics of Gaussian quantum steering in coupled lossy optical waveguides using the covariance matrix formalism. Optical dissipation is explicitly incorporated to account for realistic propagation losses in coupled waveguides. We systematically investigate the influence of the optical loss rate, purity, nonclassicality, and squeezing of the input Gaussian states on the generation and evolution of steering. The results demonstrate that increasing nonclassicality and squeezing enhances Gaussian steering, while optical loss and reduced purity progressively suppress it. However, a considerable amount of steering can persist over finite propagation intervals in the presence of optical loss. We further examine that steering is symmetric for input states with identical nonclassicality, while unequal nonclassicalities lead to directional steering asymmetry, offering a way to control the steering direction through input-state engineering. These results demonstrate that coupled optical waveguides can support controllable Gaussian quantum steering under practical loss conditions and offer a promising integrated-photonic platform for asymmetric quantum-information protocols, including 1SDI quantum key distribution (QKD) and quantum communication.

quant-pharXiv:2609.22815•Sep 22, 2026•0 citations
Quantum steering refers to the apparent possibility of exploiting nonseparable quantum correlations to remotely influence the quantum state of an observer via local measurements. Different from entanglement and Bell nonlocality, quantum steering exhibits an inherent asymmetric property, which makes it relevant for many asymmetric quantum information processing tasks. Here, we study Gaussian quantum steering between two mechanical modes in an optomechanical ring cavity. Using experimentally feasible parameters, we show that the state of the two considered modes can exhibit two-way steering and even one-way steering. Instead of using unbalanced losses or noises, we propose a simple practical way to control the direction of one-way steering. A comparative study between the steering and entanglement of the studied modes shows that both steering and entanglement undergo a sudden death-like behavior. In particular, steering is found more fragile against thermal noise remaining constantly upper-bounded by entanglement. The proposed scheme may be meaningful for one-sided device-independent quantum key distribution, where the security of such protocol depends fundamentally on the direction of steering.
Quantum steering is a kind of quantum correlations stronger than entanglement but weaker than Bell nonlocality. In an optomechanical system pumped by squeezed light and driven in the red sideband, we study---under thermal effects---stationary Gaussian steering and its asymmetry of two mechanical modes. In the resolved sideband regime using experimentally feasible parameters, we show that Gaussian steering can be created by quantum fluctuations transfer from the squeezed light to the two mechanical modes. Moreover, one-way steering can be observed by controlling the squeezing degree or the environmental temperature. A comparative study between Gaussian steering and Gaussian R\'enyi-2 entanglement of the two considered modes shows on one hand that both steering and entanglement suffer from a sudden death-like phenomenon with early vanishing of steering in various circumstances. On the other hand, steering is found stronger than entanglement, however, remains constantly upper bounded by Gaussian R\'enyi-2 entanglement, and decays rapidly to zero under thermal noise.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum correlation and its intrinsic asymmetry makes it distinct from entanglement and Bell nonlocality. We propose here a scheme for realizing one-way Gaussian steering of two electromagnetic fields mediated by a mechanical oscillator. We reveal that the steady-state one-way steering of the intracavity and output fields is obtainable with different cavity losses or strong mechanical damping. The conditions for achieving this asymmetric steering are found, and it shows that the steering is robust against thermal mechanical fluctuations. The present scheme can realize hybrid microwave-optical asymmetric steering by optoelectromechanics. In addition, our results are generic and can also be applied to other three-mode parametrically coupled bosonic systems.
Abstract Quantum steering is a form of quantum correlation that exhibits an inherent asymmetry, distinguishing it from entanglement and Bell nonlocality. It is now understood that quantum steering plays a pivotal role in asymmetric quantum information tasks. In this work, a scheme is proposed to generate asymmetric steering between two mechanical modes by transferring quantum coherence from a correlated‐emission laser. To accomplish this, quantum Langevin equations is derived to describe the optomechanical coupling between two cavity modes and two mechanical modes along with the master equation of two‐mode laser. By examining the case where the cavity modes scatter at the anti‐Stokes sidebands, it is demonstrated that both two‐way and one‐way steering can be achieved by adjusting the strength of the field driving the gain medium of the laser. Furthermore, it is showed that the direction of one‐way steering can be controlled by varying the temperatures of the mechanical baths or the strengths of the optomechanical couplings. Additionally, it is revealed that the directionality of one‐way steering depends on the modes fluctuation levels of the modes, with the mode exhibiting larger fluctuations determining the direction. This highly controllable scheme could potentially be realized with current technology, offering a promising platform for implementing one‐way quantum information tasks.
Einstein–Podolsky–Rosen steering is a form of inseparable quantum correlations that exhibits an inherent asymmetric property, i.e. one-way steering. In this paper, we show that the radiation pressure effect can be profitably exploited to generate stationary Gaussian quantum steering between an optical cavity mode and a mechanical mode. The optical mode is driven by a blue-detuned laser within the unresolved sideband regime. Under realistic experimental conditions, we show that strong asymmetric steering can be generated between the two considered modes. Besides, we show that the direction of one-way steering can be controlled by varying the physical parameters of the system at hand (coupling, dissipation, and detuning). Also, we discuss how the generated steering can be estimated experimentally. The demonstrated optomechanical steering may have practical implications for asymmetric quantum information tasks, e.g. one-sided device-independent quantum key distribution and quantum teleportation.
Abstract We theoretically investigate the emergence and asymmetry of Gaussian quantum steering and Rényi-2 entanglement in the radiation field of a nondegenerate three-level laser system. The gain medium consists of atoms initially prepared in a coherent superposition of the upper and lower states, interacting with two quantized cavity modes coupled to a common thermal reservoir. Using the steady-state solution of the master equation and the covariance matrix formalism, we compute the Gaussian steerability in both directions and compare it to the Gaussian Rényi-2 entanglement. Our analysis reveals that, under a wide range of parameters—including gain strength, population inversion, and thermal phonon number—the system exhibits generic one-way steering from mode A to mode B , with the reverse direction being inaccessible. This asymmetry is shown to originate from the photon number imbalance between the two modes. We further demonstrate that thermal noise degrades quantum correlations, with steering being more fragile than entanglement. These results provide theoretical support for the implementation of asymmetric quantum information protocols in cavity-based platforms and could be tested with current experimental technologies.
Quantum steering is an important type of quantum correlation with potential applications in one-sided device-independent (1SDI) quantum information protocols. In this contribution, we explore the time-dependent dynamics of Gaussian quantum steering in coupled lossy optical waveguides using the covariance matrix formalism. Optical dissipation is explicitly incorporated to account for realistic propagation losses in coupled waveguides. We systematically investigate the influence of the optical loss rate, purity, nonclassicality, and squeezing of the input Gaussian states on the generation and evolution of steering. The results demonstrate that increasing nonclassicality and squeezing enhances Gaussian steering, while optical loss and reduced purity progressively suppress it. However, a considerable amount of steering can persist over finite propagation intervals in the presence of optical loss. We further examine that steering is symmetric for input states with identical nonclassicality, while unequal nonclassicalities lead to directional steering asymmetry, offering a way to control the steering direction through input-state engineering. These results demonstrate that coupled optical waveguides can support controllable Gaussian quantum steering under practical loss conditions and offer a promising integrated-photonic platform for asymmetric quantum-information protocols, including 1SDI quantum key distribution (QKD) and quantum communication.