In the present paper I formulate a framework that accommodates many unambiguous discrimination problems. I show that the prior information about any type of constituent (state, channel, or observable) allows us to reformulate the discrimination among finite number of alternatives as the discrimination among finite number of average constituents. Using this framework I solve several unambiguous tasks. I present a solution to optimal unambiguous comparison of two ensembles of unknown quantum states. I consider two cases: 1) The two unknown states are arbitrary pure states of qudits. 2) Alternatively, they are coherent states of single-mode optical fields. For this case I propose simple and optimal experimental setup composed of beam-splitters and a photodetector. As a second tasks I consider an unambiguous identification (UI) of coherent states. In this task identical quantum systems are prepared in coherent states and labeled as unknown and reference states, respectively. The promise is that one reference state is the same as the unknown state and the task is to find out unambiguously which one it is. The particular choice of the reference states is unknown to us, and only the probability distribution describing this choice is known. In a general case when multiple copies of unknown and reference states are available I propose a scheme consisting of beamsplitters and photodetectors that is optimal within linear optics. UI can be considered as a search in a quantum database, whose elements are the reference states and the query is represented by the unknown state. This perspective motivated me to show that reference states can be recovered after the measurement and might be used (with reduced success rate) in subsequent UI. Moreover, I analyze the influence of noise in preparation of coherent states on the performance of the proposed setup. Another problem I address is the unambiguous comparison of a pair of unknown qudit unitary channels. I characterize all solutions and identify the optimal ones. I prove that in optimal experiments for comparison of unitary channels the entanglement is necessary. The last task I studied is the unambiguous comparison of unknown non-degenerate projective measurements. I distinguish between measurement devices with apriori labeled and unlabeled outcomes. In both cases only the difference of the measurements can be concluded unambiguously. For the labeled case I derive the optimal strategy if each unknown measurement is used only once. However, if the apparatuses are not labeled, then each measurement device must be used (at least) twice. In particular, for qubit measurement apparatuses with unlabeled outcomes I derive the optimal test state in the two-shots scenario.
Optimum measurement for unambiguously discriminating two mixed states: General considerations and special cases
根据我们以前的出版物[U。赫尔佐格和J. A. Bergou，Phys.Rev. A 71，050301（R）（2005）]，我们研究了用于以给定先验概率出现的两个混合量子态的明确区分的最佳测量。非正交态的非生物识别是可能的概率的方式，在不确定的结果，测量失败的非零概率为代价。随着一般问题的讨论，我们给出一个例子来说明我们的解决方法。我们还提供了一般的最小可实现的故障概率不等式，并讨论了更详细的必要条件，必须满足时，其绝对下限，比例的保真度的国家，可以达到。
Experimental demonstration of optimal measurement for unambiguously discriminating asymmetric qudit states
Center for Quantum Technology, Korea Institute of Science and Technology (KIST)（韩国科学技术院量子技术中心）；Division of Quantum Information, KIST School, University of Science and Technology（韩中科技大学KIST学院量子信息系）；Department of Applied Physics, Kyung Hee University（庆熙大学应用物理系）
A class of unambiguous state discrimination problems achievable by separable measurements but impossible by local operations and classical communication
Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements
我们推导出，并通过实验证明，一个明确的相位估计与精确缩放的海森堡限制，不需要自适应测量的干涉计划。也就是说，在没有相位的先验知识的情况下，我们可以获得具有标准偏差的相位的估计，该标准偏差仅是比最小物理允许值大的小常数因子。我们的计划解决了相位模糊时存在的多个通过相移，或NOON状态，用于获得改善的相位分辨率。像最近引入的自适应技术[Higgins et al 2007 Nature 450 393]一样，我们的实验在单个光子上使用相移的多个应用。通过不需要自适应测量，而是使用预定的测量序列，本方案在概念上更简单并且明显更容易实现。此外，我们展示了一个简化的自适应方案，也超过了标准的单次量子限制。
