<p>We investigate the dynamics of quantum discord for two qubits initially prepared in Bell-diagonal states and then independently interacting with the same dephasing environment, specifically random telegraph noise (RTN) and colored noise (CN). The results demonstrate that the occurrences of sudden transitions and frozen discord are closely linked to the environmental parameters. For RTN, increasing the switching rate <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6047_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$ \gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation> can delay the onset of sudden transitions. As for CN, both pure Markovian and pure non-Markovian cases are examined by dividing the integral interval into two sections, namely <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6047_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$ [\gamma _{1}, 2] $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">[</mo> <msub> <mi>γ</mi> <mn>1</mn> </msub> <mo>,</mo> <mn>2</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6047_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$ [2, \gamma _{2}] $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">[</mo> <mn>2</mn> <mo>,</mo> <msub> <mi>γ</mi> <mn>2</mn> </msub> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>. In the Markovian regime, a decrease in <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6047_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$ \alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> or an increase in <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6047_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$ \gamma _{2} $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>γ</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> can notably postpone the point of sudden transition. On the other hand, in the non-Markovian regime, multiple sudden transitions and instances of frozen discord are observed. The duration of the second freezing time interval can be extended by increasing <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6047_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$ \alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> or decreasing <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6047_Article_IEq7.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$ \gamma _{1} $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>γ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>.</p>

Sudden Transition and Freezing of Quantum Discord in Colored-noise Environments

期刊论文
发表日期：

2025年6月9日

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L. H. Wu,
A. C. Yang,
W. W. Cheng

摘要

We investigate the dynamics of quantum discord for two qubits initially prepared in Bell-diagonal states and then independently interacting with the same dephasing environment, specifically random telegraph noise (RTN) and colored noise (CN). The results demonstrate that the occurrences of sudden transitions and frozen discord are closely linked to the environmental parameters. For RTN, increasing the switching rate $ \gamma $ $γ$ can delay the onset of sudden transitions. As for CN, both pure Markovian and pure non-Markovian cases are examined by dividing the integral interval into two sections, namely $ [\gamma _{1}, 2] $ $[γ_{1}, 2]$ and $ [2, \gamma _{2}] $ $[2, γ_{2}]$ . In the Markovian regime, a decrease in $ \alpha $ $α$ or an increase in $ \gamma _{2} $ $γ_{2}$ can notably postpone the point of sudden transition. On the other hand, in the non-Markovian regime, multiple sudden transitions and instances of frozen discord are observed. The duration of the second freezing time interval can be extended by increasing $ \alpha $ $α$ or decreasing $ \gamma _{1} $ $γ_{1}$ .