<p>This work pioneers a universal framework for quantifying quantum entanglement in nuclear systems by innovatively integrating quantum distance metrics and machine learning. We introduce a framework for quantifying entanglement in nuclear spin systems using quantum distance measures (fidelity, trace distance and Bures distance (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$D_\textrm{B}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mtext>B</mtext> </msub> </math></EquationSource> </InlineEquation>) ). A universal scaling law <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$D_\textrm{B} \propto \Gamma ^{-0.85}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>D</mi> <mtext>B</mtext> </msub> <mo>∝</mo> <msup> <mi mathvariant="normal">Γ</mi> <mrow> <mo>-</mo> <mn>0.85</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> links Bures distance to nuclear decay width, experimentally validated in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$^{56}\text {Fe}(n,\gamma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>56</mn> </mmultiscripts> <mtext>Fe</mtext> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> reactions (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$D_\textrm{B} = 0.62 \pm 0.04$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>D</mi> <mtext>B</mtext> </msub> <mo>=</mo> <mn>0.62</mn> <mo>±</mo> <mn>0.04</mn> </mrow> </math></EquationSource> </InlineEquation>). Machine learning achieves 94% prediction accuracy, revealing 18% entanglement enhancement near shell closures. Three entanglement phases guide quantum technology applications: <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$^{56}\text {Fe}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>56</mn> </mmultiscripts> <mtext>Fe</mtext> </mrow> </math></EquationSource> </InlineEquation> for memory (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$D_\textrm{B}>0.6$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>D</mi> <mtext>B</mtext> </msub> <mo>></mo> <mn>0.6</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\tau _D\sim 10^{-25}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>τ</mi> <mi>D</mi> </msub> <mo>∼</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>25</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> s) and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$^{6}\text {Li}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>6</mn> </mmultiscripts> <mtext>Li</mtext> </mrow> </math></EquationSource> </InlineEquation> for sensing. The study bridges quantum information theory and nuclear physics, offering transformative tools for both fields.</p>

Quantum distance measures in entanglement theory and nuclear spin systems

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发表日期：

2026年3月11日

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Hossein Sadeghi,
Mehdi Mirzaee

摘要

This work pioneers a universal framework for quantifying quantum entanglement in nuclear systems by innovatively integrating quantum distance metrics and machine learning. We introduce a framework for quantifying entanglement in nuclear spin systems using quantum distance measures (fidelity, trace distance and Bures distance ( $D_\textrm{B}$ $D_{B}$ ) ). A universal scaling law $D_\textrm{B} \propto \Gamma ^{-0.85}$ $D_{B} \propto Γ^{- 0.85}$ links Bures distance to nuclear decay width, experimentally validated in $^{56}\text {Fe}(n,\gamma )$ $^{56} Fe (n, γ)$ reactions ( $D_\textrm{B} = 0.62 \pm 0.04$ $D_{B} = 0.62 \pm 0.04$ ). Machine learning achieves 94% prediction accuracy, revealing 18% entanglement enhancement near shell closures. Three entanglement phases guide quantum technology applications: $^{56}\text {Fe}$ $^{56} Fe$ for memory ( $D_\textrm{B}>0.6$ $D_{B} > 0.6$ , $\tau _D\sim 10^{-25}$ $τ_{D} \sim 10^{- 25}$ s) and $^{6}\text {Li}$ $^{6} Li$ for sensing. The study bridges quantum information theory and nuclear physics, offering transformative tools for both fields.