发表机构
School of Physical Sciences, University of Chinese Academy of Sciences; ICTP-AP, University of Chinese Academy of Sciences（中国科学院大学物理科学学院; 中国科学院大学 ICTP-AP）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过径向能量壳层粗粒化Wigner函数，纠正了真空majorization猜想，并利用该关系结合部分转置提出无需态重构的双模纠缠判据。
AI 中文摘要
量子不确定性限制了Wigner函数在相空间中的集中程度。通常猜想真空Wigner函数连续地majorizes任何Wigner正定态。然而，通过构造具有局部量子相干性的Wigner正定态，使其Wigner熵低于真空值，我们证明该猜想是错误的。我们通过将单模Wigner函数在同心径向能量壳层上积分，在有限分辨率下恢复真空majorization，得到对所有Wigner正定态以及具有非负壳层权重的Wigner负定态均被真空的概率向量所majorized的概率向量。将这些壳层锚定到固定振荡器框架会破坏仿射辛不变性，使得该关系对每个非真空高斯纯态都是严格的。对于Wigner负定态，负壳层权重的持续性定义了一个径向负性尺度，对于高激发Fock态具有Airy边缘半经典渐近行为。在操作上，我们将majorization关系与部分转置相结合，得到一个双模纠缠判据，可直接从径向分箱的联合零差测量结果中评估，无需态重构。
英文摘要
Quantum uncertainty limits how strongly Wigner functions can concentrate in phase space. It is commonly conjectured that the vacuum Wigner function continuously majorizes that of any Wigner-positive state. However, by constructing Wigner-positive states whose localized quantum coherence lowers their Wigner entropy below the vacuum value, we show that this conjecture is incorrect. We restore vacuum majorization at finite resolution by integrating single-mode Wigner functions over concentric radial energy shells, obtaining probability vectors majorized by that of the vacuum for all Wigner-positive states and for Wigner-negative states with non-negative shell weights. Anchoring these shells to a fixed oscillator frame breaks affine symplectic invariance, rendering this relation strict for every non-vacuum Gaussian pure state. For Wigner-negative states, the persistence of negative shell weights defines a radial negativity scale with Airy-edge semiclassical asymptotics for highly excited Fock states. Operationally, we combine the majorization relation with partial transposition to obtain a two-mode entanglement criterion directly evaluable from radially binned joint homodyne outcomes without state reconstruction.
