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<p>The integrated negativity of the Wigner function, a computable and experimentally measurable indicator of nonclassicality linked to quantum speedup, non-Gaussianity, contextuality, and tunneling, has rarely been obtained in analytical form. Here we derive an analytical expression for the Wigner function negativity of single-mode states with at most one excitation, as well as for those obtained from them through linear symplectic transformations. Within this two-dimensional manifold, the states can be represented as points inside or on the surface of a Bloch sphere, and we show that those with a positive Wigner function form an ellipsoid inscribed within it. Furthermore, we establish a strong correlation between Wigner negativity and the trace-distance negativity, an alternative quantifier that is easier to access experimentally.</p>

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Analytic Wigner Negativity for Mixtures and Superpositions of the Lowest Fock States

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • K. M. Fonseca Romero

摘要

The integrated negativity of the Wigner function, a computable and experimentally measurable indicator of nonclassicality linked to quantum speedup, non-Gaussianity, contextuality, and tunneling, has rarely been obtained in analytical form. Here we derive an analytical expression for the Wigner function negativity of single-mode states with at most one excitation, as well as for those obtained from them through linear symplectic transformations. Within this two-dimensional manifold, the states can be represented as points inside or on the surface of a Bloch sphere, and we show that those with a positive Wigner function form an ellipsoid inscribed within it. Furthermore, we establish a strong correlation between Wigner negativity and the trace-distance negativity, an alternative quantifier that is easier to access experimentally.