Streltsov A, Chitambar E, Rana S, Bera M N, Winter A, Lewenstein M
ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain.
Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, D-14195 Berlin, Germany.
Phys Rev Lett. 2016 Jun 17;116(24):240405. doi: 10.1103/PhysRevLett.116.240405.
Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging, where two parties aim to merge their tripartite quantum state parts. In standard quantum state merging, entanglement is considered to be an expensive resource, while local quantum operations can be performed at no additional cost. However, recent developments show that some local operations could be more expensive than others: it is reasonable to distinguish between local incoherent operations and local operations which can create coherence. This idea leads us to the task of incoherent quantum state merging, where one of the parties has free access to local incoherent operations only. In this case the resources of the process are quantified by pairs of entanglement and coherence. Here, we develop tools for studying this process and apply them to several relevant scenarios. While quantum state merging can lead to a gain of entanglement, our results imply that no merging procedure can gain entanglement and coherence at the same time. We also provide a general lower bound on the entanglement-coherence sum and show that the bound is tight for all pure states. Our results also lead to an incoherent version of Schumacher compression: in this case the compression rate is equal to the von Neumann entropy of the diagonal elements of the corresponding quantum state.
理解分布式场景中的资源消耗是量子信息理论的主要目标之一。这种场景的一个突出例子是量子态合并任务，其中两方旨在合并他们的三方量子态部分。在标准量子态合并中，纠缠被认为是一种昂贵的资源，而本地量子操作可以无额外成本地执行。然而，最近的进展表明，一些本地操作可能比其他操作更昂贵：区分本地非相干操作和能够产生相干性的本地操作是合理的。这个想法引导我们进入非相干量子态合并任务，其中一方只能自由使用本地非相干操作。在这种情况下，该过程的资源由纠缠和相干对来量化。在这里，我们开发了用于研究这个过程的工具，并将它们应用于几个相关场景。虽然量子态合并可以导致纠缠增益，但我们的结果表明，没有合并过程可以同时获得纠缠和相干性。我们还给出了纠缠 - 相干和的一般下限，并表明该下限对于所有纯态都是紧的。我们的结果还导致了舒马赫压缩的非相干版本：在这种情况下，压缩率等于相应量子态对角元素的冯·诺依曼熵。
