论文标题
牛顿的身份和痕迹级积分运营商的积极性
Newton's identities and positivity of trace class integral operators
论文作者
论文摘要
我们基于基本对称的多项式提供了一组可数的条件，这些条件是必要和足够的，足以使痕量类积分运算符成为正半决赛，这是相位空间表示中量子理论的重要基石。我们还根据牛顿的身份提出了一种新的，有效的可计算算法。我们对阳性的检验比线性熵和罗伯逊·史克·丁格（Robertson-Schrödinger）的不确定性关系更敏感。我们的第一个条件等于线性熵的非负性。
We provide a countable set of conditions based on elementary symmetric polynomials that are necessary and sufficient for a trace class integral operator to be positive semidefinite, which is an important cornerstone for quantum theory in phase-space representation. We also present a new, efficiently computable algorithm based on Newton's identities. Our test of positivity is much more sensitive than the ones given by the linear entropy and Robertson-Schrödinger's uncertainty relations; our first condition is equivalent to the non-negativity of the linear entropy.
