Zhao Ming-Jing, Pereira Rajesh, Ma Teng, Fei Shao-Ming
School of Science, Beijing Information Science and Technology University, Beijing, 100192, People's Republic of China.
Department of Mathematics and Statistics, University of Guelph, Guelph, N1G2W1, Canada.
Sci Rep. 2021 Mar 15;11(1):5935. doi: 10.1038/s41598-021-85273-8.
Coherence and entanglement are fundamental concepts in resource theory. The coherence (entanglement) of assistance is the coherence (entanglement) that can be extracted assisted by another party with local measurement and classical communication. We introduce and study the general coherence of assistance. First, in terms of real symmetric concave functions on the probability simplex, the coherence of assistance and the entanglement of assistance are shown to be in one-to-one correspondence. We then introduce two classes of quantum states: the assisted maximally coherent states and the assisted maximally entangled states. They can be transformed into maximally coherent or entangled pure states with the help of another party using local measurement and classical communication. We give necessary conditions for states to be assisted maximally coherent or assisted maximally entangled. Based on these, a unified framework between coherence and entanglement including coherence (entanglement) measures, coherence (entanglement) of assistance, coherence (entanglement) resources is proposed. Then we show that the coherence of assistance as well as entanglement of assistance are strictly larger than the coherence of convex roof and entanglement of convex roof for all full rank density matrices. So all full rank quantum states are distillable in the assisted coherence distillation.
相干性和纠缠是资源理论中的基本概念。辅助相干性（纠缠）是指在另一方进行局域测量和经典通信辅助下能够提取的相干性（纠缠）。我们引入并研究了一般的辅助相干性。首先，在概率单纯形上的实对称凹函数方面，辅助相干性和辅助纠缠被证明是一一对应的。然后我们引入两类量子态：辅助最大相干态和辅助最大纠缠态。它们可以在另一方使用局域测量和经典通信的帮助下转换为最大相干或纠缠的纯态。我们给出了态为辅助最大相干或辅助最大纠缠的必要条件。基于此，提出了一个包括相干（纠缠）度量、辅助相干（纠缠）、相干（纠缠）资源在内的相干性和纠缠之间的统一框架。然后我们表明，对于所有满秩密度矩阵，辅助相干性以及辅助纠缠都严格大于凸包相干性和凸包纠缠。所以在辅助相干蒸馏中所有满秩量子态都是可蒸馏的。
