标题： 量子线性光学中的李代数不变量 显示英文标题

标题： Lie algebraic invariants in quantum linear optics

摘要： 量子线性光学是获得量子计算优势的有希望的候选方案。 然而，没有后选择的线性光学不足以从给定的输入状态生成任何量子态。 这限制了其用途，因为一些计算需要难以准备的纠缠资源。 因此，我们需要对线性光学态制备有更深入的理解。 在本工作中，我们提供了一种方法，用于推导任意态在任何可能的无源线性干涉仪演化中的守恒量。 我们通过将态的密度算符投影到无源线性光学哈密顿量的李代数上，得到了这些不变量。 这些不变量的守恒为使用无源线性光学进行精确和近似态制备提供了必要条件：如果输入态和输出态具有不同的不变量，则无法设计一个线性光学实验将其中一个演化为另一个或足够接近的态。 因此，这些不变量使我们在尝试从易于制备的态（如福克态）制备对量子信息有用的纠缠态（如贝尔态或NOON态）时，能够缩小搜索范围。 我们得出结论，未来的精确和近似态制备方法需要考虑由我们的不变量给出的必要条件，以排除不可能的线性光学演化。 显示英文摘要

摘要： Quantum linear optics is a promising candidate for obtaining a quantum computational advantage. However, linear optics without post-selection is not powerful enough to produce any quantum state from a given input state. This limits its utility since some computations require entangled resources that are difficult to prepare. Thus, we need a deeper understanding of linear optical state preparation. In this work, we give a recipe to derive conserved quantities in the evolution of arbitrary states along any possible passive linear interferometer. We obtain the invariants by projecting the density operator of the state onto the Lie algebra of passive linear optical Hamiltonians. The conservation of the invariants gives necessary conditions for exact and approximate state preparation with passive linear optics: if input and output states have different invariants, it will be impossible to design a linear optical experiment that evolves one into the other or a sufficiently close one. Therefore, the invariants allow us to narrow the search when trying to prepare entangled states useful for quantum information, like Bell or NOON states, from easy-to-prepare states, like Fock states. We conclude that future exact and approximate state preparation methods will need to take into account the necessary conditions given by our invariants to weed out impossible linear optical evolutions.