Monogamy of Gaussian quantum steering and entanglement in a hybrid qubit-cavity optomagnonic system with coherent feedback loop

TL;DR

The paper addresses how monogamy constraints govern Gaussian steering and genuine tripartite entanglement in a hybrid qubit–cavity optomagnonic system with a coherent feedback loop under finite temperature. Using a linearized Gaussian-state framework, it derives a six-dimensional covariance matrix by solving a Lyapunov equation and quantifies correlations with logarithmic negativity and Gaussian steering measures, verifying CKW-type monogamy inequalities for steering. The study shows that coherent feedback enhances entanglement and one-way steering, and that steering monogamy remains valid across parameter ranges, though correlations decay with increasing temperature. These results suggest that feedback-enabled hybrid magnon–photon–qubit platforms offer a route to robust quantum networks resilient to thermal noise.

Abstract

The monogamy of quantum correlations is a fundamental principle in quantum information processing, limiting how quantum correlations can be shared among multiple subsystems. Here we propose a theoretical scheme to investigate the monogamy of quantum steering and genuine tripartite entanglement in a hybrid qubit-cavity optomagnonic system with a coherent feedback loop. Using logarithmic negativity and Gaussian quantum steering, we quantify entanglement and steerability, respectively. We verify the CKW-type monogamy inequalities which leads to steering monogamous through adjustments of the reflective parameter among three tripartite modes versus temperature. Our results show that a coherent feedback loop can enhance entanglement and quantum steering under thermal effects.

Figures (7)

• Figure 1: (a) A schematic of the hybrid cavity-qubit optomagnonic system using coherent feedback loop. The ferromagnetic YIG sphere, which contains the collective motion of spins representing the magnons, is placed inside the cavity's optical whispering gallery mode (WGM) ($c$). An external magnetic field $B_0$ is applied along the z-axis. The cavity is driven by an input electromagnetic field with amplitude $\mathcal{A}$ through an asymmetric beam splitter (BS) with transmission and reflection coefficients $u$ and $\epsilon$, respectively. (b) The interaction among the subsystems. The cavity is coupled to the superconducting qubit ($q$) with a coupling strength $g_q$ and to the magnon mode ($m$) with a coupling strength $g_m$.
• Figure 2: Plot of the bipartite entanglement (logarithmic negativity, $\mathcal{L}$) for three mode pairs---cavity-magnon ($\mathcal{L}_{cm}$), cavity-qubit ($\mathcal{L}_{cq}$), and magnon-qubit ($\mathcal{L}_{mq}$)---as a function of temperature $T$. The subfigures correspond to two different reflectivity values: (a) $\epsilon=0$ and (b) $\epsilon=0.86$. The other parameters are set to $\Gamma/2\pi=0.2\times10^6$ Hz and $g_q/\tilde{g}_m=2$.
• Figure 3: Plot of bipartite entanglement, Gaussian quantum steering, and asymmetric quantum steering as a function of temperature $T$. The subfigures display the results for: (a) the cavity-qubit pair ($\mathcal{L}_{cq}$, $\mathcal{G}^{c\to q}$, $\mathcal{G}^{q\to c}$, and $\mathcal{G}(cq)$), (b) the cavity-magnon pair ($\mathcal{L}_{cm}$, $\mathcal{G}^{c\to m}$, $\mathcal{G}^{m\to c}$, and $\mathcal{G}(cm)$), and (c) the qubit-magnon pair ($\mathcal{L}_{qm}$, $\mathcal{G}^{q\to m}$, $\mathcal{G}^{m\to q}$, and $\mathcal{G}(qm)$). The parameters are set to $\Gamma/2\pi=0.2\times10^6$ Hz, $\epsilon=0.86$, $g_q/\tilde{g}_m=2$ and $\theta=\pi$.
• Figure 4: Plot tripartite entanglement $\mathbb{R}_{\text{min}}$ as function of the reflictivity parameter $\epsilon$, for different value of temperature $T$, with the parametrers $\Gamma/2\pi=0.2\times 10^{6}$Hz, $g_q/g_0=2$ and $\theta=\pi$.
• Figure 5: Plot of bipartite entanglement (logarithmic negativity, $\mathcal{L}$) for three mode pairs---cavity-magnon ($\mathcal{L}_{cm}$), cavity-qubit ($\mathcal{L}_{cq}$), and magnon-qubit ($\mathcal{L}_{mq}$)---as a function of the reflection coefficient $\epsilon$. The parameters used are $\Gamma/2\pi=0.2\times10^6$ Hz and $\theta=\pi$.