对称态中粒子子集的相关性：当忽略其余光子时，光束中的光子在做什么
Correlations for subsets of particles in symmetric states: what photons are doing within a beam of light when the rest are ignored
AI总结：
本文提出与模式无关的光子移除公式，揭示算符期望值与被检查光子数 $q$ 的关系，证明随机 $q$ 光子态系数等于原态 $q$ 阶相关函数，适用于任意完全对称态。
摘要：
给定一个光场态，当仅观察其部分组成光子而忽略（求迹掉）其余光子时，其性质如何变化？通过开发用于从光束中移除光子的与模式无关的公式，我们展示了当仅从光束中检查 $q$ 个光子并忽略其余光子时，任意算符的期望值如何变化。我们利用这一点，用随机选择 $q$ 个光子所得到的状态重新表达了算符的期望值。值得注意的是，这只在 $q$ 的唯一值下等于真实期望值：将算符表示为正规序形式的单项式时，$q$ 必须等于该算符湮灭的光子数。一个有用的推论是，从任意态中随机选择的任意 $q$ 光子态的系数，恰好等于原始态的 $q$ 阶相关函数；人们可以通过检查强度矩来了解任意随机光子将做什么，反之，只需观察 $n$ 光子子空间即可辨别所有 $n$ 阶相关函数。敏锐的读者会欣喜地发现这里没有意外，只有对直觉的数学证明。我们的结果适用于任意类型粒子在任意粒子数组合下的完全对称态，并可用于任何存在玻色子相关性的场合。
英文摘要：
Given a state of light, how do its properties change when only some of the constituent photons are observed and the rest are neglected (traced out)? By developing formulae for mode-agnostic removal of photons from a beam, we show how the expectation value of any operator changes when only $q$ photons are inspected from a beam, ignoring the rest. We use this to reexpress expectation values of operators in terms of the state obtained by randomly selecting $q$ photons. Remarkably, this only equals the true expectation value for a unique value of $q$: expressing the operator as a monomial in normally ordered form, $q$ must be equal to the number of photons annihilated by the operator. A useful corollary is that the coefficients of any $q$-photon state chosen at random from an arbitrary state are exactly the $q$th order correlations of the original state; one can inspect the intensity moments to learn what any random photon will be doing and, conversely, one need only look at the $n$-photon subspace to discern what all of the $n$th order correlation functions are. The astute reader will be pleased to find no surprises here, only mathematical justification for intuition. Our results hold for any completely symmetric state of any type of particle with any combination of numbers of particles and can be used wherever bosonic correlations are found.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
