<p>We investigate the robustness of quantum-metrological usefulness for a class of highly entangled multi-qubit states, extending the framework introduced in the previous work. Our analysis focuses on the impact of two prototypical noise models, white and colored noise, on various quantum states, including GHZ, W, Dicke with multiple excitations, cluster, and ring cluster states, as well as a newly studied <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\vert {\psi _5} \rangle$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mn>5</mn> </msub> <mrow> <mo stretchy="false">⟩</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> state. The robustness is quantified via a global optimization of quantum Fisher information over arbitrary local operators. We analyze the effect of increasing qubit number and examine different local measurement strategies, comparing uniform versus individually optimized local operators. Results reveal state-dependent behavior: while states like <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\vert {GHZ_N} \rangle$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <mrow> <mi>G</mi> <mi>H</mi> <msub> <mi>Z</mi> <mi>N</mi> </msub> </mrow> <mrow> <mo stretchy="false">⟩</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\vert {W_N} \rangle$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <msub> <mi>W</mi> <mi>N</mi> </msub> <mrow> <mo stretchy="false">⟩</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> exhibit increasing robustness under colored noise and decreasing robustness under white noise, the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\vert {\psi _5} \rangle$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mn>5</mn> </msub> <mrow> <mo stretchy="false">⟩</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> state shows improvement under both types. These findings provide new insights into designing metrologically useful states resilient to practical noise conditions.</p>

Noise-resilient quantum metrology using entangled multi-qubit states: robustness analysis and measurement strategies

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2026年3月2日

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Esraa Mishref,
Ahmed El-Tawargy,
Wael Ramadan,
Mohamed Nawareg

摘要

We investigate the robustness of quantum-metrological usefulness for a class of highly entangled multi-qubit states, extending the framework introduced in the previous work. Our analysis focuses on the impact of two prototypical noise models, white and colored noise, on various quantum states, including GHZ, W, Dicke with multiple excitations, cluster, and ring cluster states, as well as a newly studied $\vert {\psi _5} \rangle$ $| ψ_{5} ⟩$ state. The robustness is quantified via a global optimization of quantum Fisher information over arbitrary local operators. We analyze the effect of increasing qubit number and examine different local measurement strategies, comparing uniform versus individually optimized local operators. Results reveal state-dependent behavior: while states like $\vert {GHZ_N} \rangle$ $| G H Z_{N} ⟩$ and $\vert {W_N} \rangle$ $| W_{N} ⟩$ exhibit increasing robustness under colored noise and decreasing robustness under white noise, the $\vert {\psi _5} \rangle$ $| ψ_{5} ⟩$ state shows improvement under both types. These findings provide new insights into designing metrologically useful states resilient to practical noise conditions.