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： 没有后选择的量子线性光学不足以从给定的输入态生成任何量子态。 这限制了其应用，因为一些应用需要难以制备的纠缠资源。 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，我们提供了一个方法，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。 这样的不变量的一个例子是密度算符在无源线性光学哈密顿量李代数上的投影。 这些不变量给出了精确态制备的必要条件：如果输入态和输出态具有不同的不变量，则不可能设计一个无源线性干涉仪将其中一个演化为另一个。 此外，我们基于它们的不变量之间的距离，给出了输出态与目标态之间距离的下限。 这为近似或后选择态制备提供了必要条件。 因此，这些不变量使我们在尝试从易于制备的态（如福克态）制备有用的纠缠态（如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 without post-selection is not powerful enough to produce any quantum state from a given input state. This limits its utility since some applications 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. One example of such an invariant is the projection of a density operator onto the Lie algebra of passive linear optical Hamiltonians. These invariants give necessary conditions for exact state preparation: if the input and output states have different invariants, it is impossible to design a passive linear interferometer that evolves one into the other. Moreover, we provide a lower bound to the distance between an output and target state based on the distance between their invariants. This gives a necessary condition for approximate or heralded state preparations. Therefore, the invariants allow us to narrow the search when trying to prepare useful entangled states, like NOON states, from easy-to-prepare states, like Fock states. We conclude that future exact and approximate state preparation methods will need to consider the necessary conditions given by our invariants to weed out impossible linear optical evolutions.