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<p>Quantum information processing promises significant advantages over classical methods but remains vulnerable to decoherence induced by environmental interactions and spacetime effects. This work investigates the behavior of Quantum Fisher Information (QFI) as a diagnostic tool for entanglement and parameter estimation in a three-qubit entangled Dirac system subjected to dissipative noisy channels in the curved spacetime of a Schwarzschild black hole. In particular, we examine the influence of the squeezed generalized amplitude damping (SGAD) channel, along with its subchannels– generalized amplitude damping (GAD) and amplitude damping (AD)– on the QFI with respect to entanglement weight (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta\)</EquationSource> </InlineEquation>) and phase (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi\)</EquationSource> </InlineEquation>) parameters. Our results show that under strong squeezing (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(r = 1\)</EquationSource> </InlineEquation>), the QFI with respect to <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta\)</EquationSource> </InlineEquation> becomes completely resistant to variations in the Hawking temperature (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_H\)</EquationSource> </InlineEquation>), while still exhibiting degradation with increasing channel temperature (<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_C\)</EquationSource> </InlineEquation>). The QFI decay is significantly slower at <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(r = 1\)</EquationSource> </InlineEquation> compared to <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq8.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(r = 0\)</EquationSource> </InlineEquation>, suggesting that squeezing can function as an error mitigation strategy. For QFI with respect to <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi\)</EquationSource> </InlineEquation>, a transient spike is observed at <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_C = 2\)</EquationSource> </InlineEquation>, potentially due to thermal resonance or non-monotonic decoherence, and this behavior is unaffected by <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_H\)</EquationSource> </InlineEquation>. Similar patterns are noted in the GAD and AD channels, where <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6073_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_C\)</EquationSource> </InlineEquation> consistently dominates as the principal source of decoherence. Overall, the results highlight the intricate interplay between environmental noise, relativistic effects, and quantum error resilience in curved spacetime.</p>

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Quantum Fisher Information in Curved Spacetime: Dirac Particles in Noisy Channels around a Schwarzschild Black Hole

  • 期刊论文

  • 发表日期：

    2025年7月18日

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  • Cookey Iyen,
  • Muhammad Sanusi Liman,
  • Benedict O. Ayomanor,
  • Emem-obong Solomon James,
  • Yame Mwanzang Philemon,
  • Babatunde James Falaye

摘要

Quantum information processing promises significant advantages over classical methods but remains vulnerable to decoherence induced by environmental interactions and spacetime effects. This work investigates the behavior of Quantum Fisher Information (QFI) as a diagnostic tool for entanglement and parameter estimation in a three-qubit entangled Dirac system subjected to dissipative noisy channels in the curved spacetime of a Schwarzschild black hole. In particular, we examine the influence of the squeezed generalized amplitude damping (SGAD) channel, along with its subchannels– generalized amplitude damping (GAD) and amplitude damping (AD)– on the QFI with respect to entanglement weight ( \(\theta\) ) and phase ( \(\phi\) ) parameters. Our results show that under strong squeezing ( \(r = 1\) ), the QFI with respect to \(\theta\) becomes completely resistant to variations in the Hawking temperature ( \(T_H\) ), while still exhibiting degradation with increasing channel temperature ( \(T_C\) ). The QFI decay is significantly slower at \(r = 1\) compared to \(r = 0\) , suggesting that squeezing can function as an error mitigation strategy. For QFI with respect to \(\phi\) , a transient spike is observed at \(T_C = 2\) , potentially due to thermal resonance or non-monotonic decoherence, and this behavior is unaffected by \(T_H\) . Similar patterns are noted in the GAD and AD channels, where \(T_C\) consistently dominates as the principal source of decoherence. Overall, the results highlight the intricate interplay between environmental noise, relativistic effects, and quantum error resilience in curved spacetime.