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arXiv:2609.22815

Asymmetric Two-Way Gaussian Quantum Steering in Coupled Lossy Waveguides

Hafsa Zia, Haleema Sadia Qureshi, Shakir Ullah, Mohamed Amazioug, Fazal Ghafoor

quant-phSubmitted Sep 19, 2026• Announced Sep 22, 2026• 0 citations
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Abstract

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.

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Modern Physics Letters A•Feb 9, 2024•1 citation
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.
Nonlocal correlations, a longstanding foundational topic in quantum information, have recently found application as a resource for cryptographic tasks where not all devices are trusted, for example in settings with a highly secure central hub, such as a bank or government department, and less secure satellite stations which are inherently more vulnerable to hardware "hacking" attacks. The asymmetric phenomena of Einstein-Podolsky-Rosen steering plays a key role in one-sided device-independent quantum key distribution (1sDI-QKD) protocols. In the context of continuous-variable (CV) QKD schemes utilizing Gaussian states and measurements, we identify all protocols that can be 1sDI and their maximum loss tolerance. Surprisingly, this includes a protocol that uses only coherent states. We also establish a direct link between the relevant EPR steering inequality and the secret key rate, further strengthening the relationship between these asymmetric notions of nonlocality and device independence. We experimentally implement both entanglement-based and coherent-state protocols, and measure the correlations necessary for 1sDI key distribution up to an applied loss equivalent to 7.5 km and 3.5 km of optical fiber transmission respectively. We also engage in detailed modelling to understand the limits of our current experiment and the potential for further improvements. The new protocols we uncover apply the cheap and efficient hardware of CVQKD systems in a significantly more secure setting.
In this work, we investigate continuous-variable (CV) quantum steering in a genuine bimodal active Raman-driven quantum beat laser (RDQBL) system. The lasing medium of the system is coupled to two external classical fields in Raman configuration and to two quantized cavity modes, the latter being initially prepared in arbitrary single-mode Gaussian states. Using the reduced density matrix of the evolved cavity modes, we derive and solve the dynamical equations analytically and numerically. We analyze the time evolution and strength of quantum steering in the two-mode Gaussian states against various system parameters, for instance, the intensity and relative phase of the classical Raman fields, the cavity decay rates, and the non-classicality and purity of the input cavity modes. Our results show that the cavity modes exhibit robust, tunable steerability across a wide range of parameters. We further demonstrate the intrinsic asymmetry of quantum steering, that is, an imbalance in the non-classicality of input modes ( τ 1 ≠ τ 2 ) leads to one-way directional steering. These findings establish the RDQBL system as a promising platform for controllable CV quantum steering with potential applications in secure quantum communication, quantum key distribution (QKD), quantum metrology, and asymmetric quantum networks.
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.
We present a comprehensive phase diagram of quantum correlations in a three-mode Gaussian state generated by a tritter, driven by a two-mode squeezed vacuum and a coherent state. The coherent amplitude does not affect the correlation structure, which is solely governed by the initial squeezing. By systematically analyzing five physically relevant asymmetric loss configurations, we map out the exact resilience thresholds for entanglement and Einstein-Podolsky-Rosen (EPR) steering under all bipartite partitions. We reveal that EPR steering exhibits a pronounced directional asymmetry under loss, and its survival can be maintained over a much wider range of loss by strategically protecting a single channel. This tunable fragility provides practical guidance for one-sided device-independent quantum protocols in noisy asymmetric networks. We further confirm the limitations of Rényi-2 entropy in the quantification of entanglement and steering. Our results transform the abstract correlation hierarchy into a calculable, experimentally relevant guide for engineering robust quantum resources.
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.
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.