The presence of an absorber in one of the paths of an interferometer changes the output statistics of that interferometer in a fundamental manner. Since the individual quantum particles detected at any of the outputs of the interferometer have not been absorbed, any non-trivial effect of the absorber on the distribution of these particles over these paths is a counterfactual effect. Here, we quantify counterfactual effects by evaluating the information about the presence or absence of the absorber obtained from the output statistics, distinguishing between classical and quantum counterfactual effects. We identify the counterfactual gain which quantifies the advantage of quantum counterfactual protocols over classical counterfactual protocols, and show that this counterfactual gain can be separated into two terms: a semi-classical term related to the amplitude blocked by the absorber, and a Kirkwood-Dirac quasiprobability assigning a joint probability to the blocked path and the output port. A negative Kirkwood-Dirac term between a path and an output port indicates that inserting the absorber into that path will have a focussing effect, increasing the probability of particles arriving at that output port, resulting in a significant enhancement of the counterfactual gain. We show that the magnitude of quantum counterfactual effects cannot be explained by a simple removal of the absorbed particles, but originates instead from a well-defined back-action effect caused by the presence of the absorber in one path, on particles in other paths.

中文翻译：

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多路径干涉仪中的反事实、反作用和信息增益


干涉仪路径之一中吸收体的存在从根本上改变了该干涉仪的输出统计数据。由于在干涉仪的任何输出处检测到的单个量子粒子都没有被吸收，因此吸收器对这些粒子在这些路径上的分布的任何重要影响都是反事实的影响。在这里，我们通过评估从输出统计中获得的吸收体是否存在的信息来量化反事实效应，区分经典反事实效应和量子反事实效应。我们确定了反事实增益，它量化了量子反事实协议相对于经典反事实协议的优势，并表明这种反事实增益可以分为两项：与吸收器阻挡的幅度相关的半经典项和柯克伍德-狄拉克准概率为阻塞路径和输出端口分配联合概率。路径和输出端口之间的负柯克伍德-狄拉克项表明，将吸收器插入该路径将产生聚焦效应，增加粒子到达该输出端口的概率，从而显着增强反事实增益。我们表明，量子反事实效应的大小不能通过简单地去除被吸收的粒子来解释，而是源于由于一条路径中吸收体的存在而对其他路径中的粒子造成的明确的反作用效应。