<p>Numerous strategies have been proposed to manipulate and protect symmetric quantum correlations from decoherence. However, there needs to be more emphasis on asymmetric ones, such as Einstein–Podolsky–Rosen (EPR) steering. In this study, we delve into EPR steering between two frequency-modulated qubits coupled to a zero-temperature reservoir individually, in both weak and strong coupling regimes. We consider a scenario where each qubit is locally identically coupled to its environment. The results demonstrate that the decay of EPR steering between the two qubits can be delayed remarkably by controlling frequency modulation parameters, regardless of whether the system exhibits Markovian or non-Markovian behavior. Moreover, we observe that a precise balance between modulation strength <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4946_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation> and frequency <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4946_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$\varOmega $</EquationSource> <EquationSource Format="MATHML"><math> <mi>Ω</mi> </math></EquationSource> </InlineEquation>, determining the zeros of the Bessel function <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4946_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">$J_{0}(\delta /\varOmega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>J</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">/</mo> <mi>Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, can significantly enhance EPR steering in the strong coupling regime. Furthermore, we investigate the asymmetric nature of EPR steering by examining a scenario where one of the qubits remains unmodulated. We thoroughly analyze the impact of modulation parameters on the occurrence of EPR steering sudden death. The findings highlight that asymmetry properties, such as one-way and two-way steering, can be effectively manipulated by adjusting the frequency modulation parameters, even when the initial two-qubit state is symmetrical. These results suggest that it is feasible to safeguard EPR steering and control its asymmetry properties without requiring additional quantum resources.</p>

Frequency modulation-controlled Einstein–Podolsky–Rosen steering in leaky cavities

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发表日期：

2025年10月3日

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S. J. Chen,
D. C. Qian,
Y. H. Sun,
M. K. Wu,
W. W. Cheng

摘要

Numerous strategies have been proposed to manipulate and protect symmetric quantum correlations from decoherence. However, there needs to be more emphasis on asymmetric ones, such as Einstein–Podolsky–Rosen (EPR) steering. In this study, we delve into EPR steering between two frequency-modulated qubits coupled to a zero-temperature reservoir individually, in both weak and strong coupling regimes. We consider a scenario where each qubit is locally identically coupled to its environment. The results demonstrate that the decay of EPR steering between the two qubits can be delayed remarkably by controlling frequency modulation parameters, regardless of whether the system exhibits Markovian or non-Markovian behavior. Moreover, we observe that a precise balance between modulation strength $\delta $ $δ$ and frequency $\varOmega $ $Ω$ , determining the zeros of the Bessel function $J_{0}(\delta /\varOmega )$ $J_{0} (δ / Ω)$ , can significantly enhance EPR steering in the strong coupling regime. Furthermore, we investigate the asymmetric nature of EPR steering by examining a scenario where one of the qubits remains unmodulated. We thoroughly analyze the impact of modulation parameters on the occurrence of EPR steering sudden death. The findings highlight that asymmetry properties, such as one-way and two-way steering, can be effectively manipulated by adjusting the frequency modulation parameters, even when the initial two-qubit state is symmetrical. These results suggest that it is feasible to safeguard EPR steering and control its asymmetry properties without requiring additional quantum resources.