Absorption-free (also known as ``interaction-free'') measurement aims to detect the presence of an opaque object using a test particle without that particle being absorbed by the object. Here we consider semi-transparent objects which have an amplitude $α$ of transmitting a particle while leaving the state of the object unchanged and an amplitude $β$ of absorbing the particle. The task is to devise a protocol that can decide which of two known transmission amplitudes is present while ensuring that no particle interacts with the object. We show that the probabilities of being able to achieve this are limited by an inequality. This inequality implies that absorption free distinction between complete transparency and any partial transparency is always possible with probabilities approaching 1, but that two partial transparencies can only be distinguished with probabilities less than 1.
A Semidefinite Programming Approach to Optimal Unambiguous Discrimination of Quantum States
本文研究线性无关纯量子态的无模糊判别问题。我们表明,设计的最佳测量,最大限度地减少了不确定的结果的概率,可以制定为一个半定规划问题。基于这个公式,我们发展了一组最佳量子测量的充分必要条件。我们表明,最佳的测量可以非常有效地计算在多项式时间内利用许多著名的算法来解决半定方案,这是保证收敛到全局最优。使用最优性的一般条件,我们得到必要和充分条件,使测量结果在一个不确定的结果为每一个量子态的概率相等是最佳的。我们把这种测量称为等概率测量(Equal Probability Measurement,简称EMT)。然后,我们表明,对于任何状态集,状态的先验概率可以选择,使得最优的。最后,我们考虑具有强对称性和等先验概率的状态集,对于这些状态集,最优解是最优的。我们首先考虑定义在一组酉矩阵上的几何一致状态集,它们由单个生成向量生成。然后,我们考虑复合几何均匀状态集所产生的一组酉矩阵使用多个生成向量,其中的生成向量满足一定的(加权)范数约束。
The splitting in potential Crank-Nicolson scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip
CEA, DAM, DIF(法国原子能委员会);National Research University Higher School of Economics(国立研究型高等经济大学);National Research University Moscow Power Engineering Institute(国立研究型莫斯科动力工程学院)
A splitting higher order scheme with discrete transparent boundary conditions for the Schrödinger equation in a semi-infinite parallelepiped
CEA/DAM/DIF(法国原子能委员会 DAM DIF);National Research University Higher School of Economics(国立研究型大学高等经济大学);National Research University Moscow Power Engineering Institute(国立研究型大学莫斯科动力工程学院)
Limits for molecular spectroscopy from quantum channel discrimination
School of Science, STEM College, RMIT University(斯威本科技大学理学院STEM学院);Quantum Systems, Technology, CSIRO(澳大利亚联邦科学与工业研究组织量子系统与技术部);School of Mathematics and Physical Sciences, the University of Sheffield(谢菲尔德大学数学与物理科学学院);School of Electrical and Computer Engineering, Cornell University(康奈尔大学电气与计算机工程学院)