<p>Quantum discord, a key indicator of nonclassical correlations in bipartite systems, has been recently extended to multipartite scenarios [Phys. Rev. Lett. 2020, 124:110401]. We present exact analytic formulas for the quantum discord of special families of N-qubit states, including generalized class of GHZ states. Our formulations span 2, 3, 4<i>n</i>, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2024_4625_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$4n+1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2024_4625_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$4n+2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4</mn> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2024_4625_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$4n+3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4</mn> <mi>n</mi> <mo>+</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>-qubit configurations where <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2024_4625_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">$n\in 1, 2, \ldots $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>∈</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> </mrow> </math></EquationSource> </InlineEquation>, which refine the assessment of quantum correlations and provide an analytical tool in quantum computation. Moreover, we uncover a “discord freezing” in even-qubit systems under phase flip decoherence which provides a means for preserving quantum coherence in environmental perturbations.</p>

Analytic formulas for quantum discord of special families of N-qubit states

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发表日期：

2025年1月6日

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Jianming Zhou,
Xiaoli Hu,
Honglian Zhang,
Naihuan Jing

摘要

Quantum discord, a key indicator of nonclassical correlations in bipartite systems, has been recently extended to multipartite scenarios [Phys. Rev. Lett. 2020, 124:110401]. We present exact analytic formulas for the quantum discord of special families of N-qubit states, including generalized class of GHZ states. Our formulations span 2, 3, 4n, $4n+1$ $4 n + 1$ , $4n+2$ $4 n + 2$ , and $4n+3$ $4 n + 3$ -qubit configurations where $n\in 1, 2, \ldots $ $n \in 1, 2, \dots$ , which refine the assessment of quantum correlations and provide an analytical tool in quantum computation. Moreover, we uncover a “discord freezing” in even-qubit systems under phase flip decoherence which provides a means for preserving quantum coherence in environmental perturbations.