Title: Complementarity in Quantum Information Processing Tasks Show Chinese title

Title: 量子信息处理任务中的互补性

Abstract: Complementarity have been an intriguing feature of physical systems for a long time. In this work we establish a new kind of complimentary relations in the frame work of quantum information processing tasks. In broadcasting of entanglement we create many pairs of less entangled states from a given entangled state both by local and non local cloning operations. These entangled states can be used in various information processing tasks like teleportation and superdense coding. Since these states are less entangled states it is quite intuitive that these states are not going to be as powerful resource as the initial states. In this work we study the usefulness of these states in tasks like teleportation and super dense coding. More precisely, we found out bounds of their capabilities in terms of several complimentary relations involving fidelity of broadcasting. In principle we have considered general mixed as a resource also separately providing different examples like a) Werner like states, b) Bell diagonal states. Here we have used both local and non local cloning operations as means of broadcasting. In the later part of our work, we extend this result by obtaining bounds in form of complimentary relations in a situation where we have used $1-N$ cloning transformations instead of $1-2$ cloning transformations. Show Chinese abstract

Abstract: 互补性长期以来一直是物理系统的一个引人入胜的特征。 在这项工作中，我们在量子信息处理任务的框架内建立了新的互补关系。 在纠缠广播中，我们通过局域和非局域克隆操作从一个给定的纠缠态创建许多对纠缠较弱的状态。 这些纠缠态可以用于诸如隐形传态和超密集编码等各种信息处理任务。 由于这些状态的纠缠程度较低，因此很直观地认为它们不会像初始状态那样成为强大的资源。 在这项工作中，我们研究了这些状态在隐形传态和超密集编码任务中的有用性。 更具体地说，我们通过涉及广播保真度的几种互补关系找到了它们能力的界限。 原则上，我们还单独考虑了混合态作为资源，并提供了不同的例子，如a) 韦尔纳态（Werner-like states），b) 贝尔对角态（Bell diagonal states）。 在这里，我们使用了局域和非局域克隆操作作为广播的手段。 在我们的工作的后半部分，我们通过在使用$1-N$克隆变换而非$1-2$克隆变换的情况下获得互补关系形式的界限，扩展了这一结果。