A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum value of the purity one can get at the output of a channel by varying over all physical input states, when purity is measured by the Schatten $q$-norm, and is denoted by $ν_q$. The multiplicativity problem is the question whether two channels used in parallel have a combined $ν_q$ that is the product of the $ν_q$ of the two channels. A positive answer would imply a number of other additivity results in QIT.
Very recently, P. Hayden has found counterexamples for every value of $q>1$. Nevertheless, these counterexamples require that the dimension of these channels increases with $1-q$ and therefore do not rule out multiplicativity for $q$ in intervals $[1,q_0)$ with $q_0$ depending on the channel dimension. I argue that this would be enough to prove additivity of entanglement of formation and of the classical capacity of quantum channels.
More importantly, no counterexamples have as yet been found in the important special case where one of the channels is a qubit-channel, i.e. its input states are 2-dimensional. In this paper I focus attention to this qubit case and I rephrase the multiplicativity conjecture in the language of block matrices and prove the conjecture in a number of special cases.
最近Horodecki等人[Phys. Rev. Lett. 90，100402（2003）]介绍了一种重要的量子信息处理范例，其中共享相同二分量子态的多个副本的两方借助于由单向（双向）完全退相信道辅助的局域么正操作来提取局域纯态。从热力学的角度来看，局域纯态是一种有价值的资源，因为它们允许通过局域量子热机将热能转换为功。我们给出了一个简单的信息理论表征的单向可重复的本地纯度，这原来是密切相关的一个以前已知的操作措施的经典相关性，单向可重复的共同随机性。
Geometrical constructions of purity testing protocols and their applications to quantum communication
University of the Basque Country UPV/EHU（巴斯克地区大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络维格纳物理研究中心）；University of Szeged（塞格德大学）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）；Flinders University（弗林德斯大学）；University of Vigo（维戈大学）
Completely Bounded Qusi-Norms, Their Mutiplicativity, and New Additivity Results of Quantum Channels
Institute for Advanced Study in Mathematics, Harbin Institute of Technology（哈尔滨工业大学高等研究院）；Laboratoire de Mathématiques, Université Marie & Louis Pasteur（玛丽·路易·巴斯德大学数学实验室）
Calculus of Robinet: completely positive reconstruction of time-averaged diffusive quantum trajectories
Laboratoire de Physique de l’École Normale Supérieure - PSL, Centre Automatique et Systèmes Mines Paris - PSL, CNRS, Inria, PSL Research University（巴黎高等师范学院物理实验室、巴黎高等矿业学院自动与系统中心、法国国家科学研究中心、法国国家信息与自动化研究所、巴黎文理研究大学）
Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology（国际信息技术学院计算自然科学与生物信息中心）；International Institute of Information Technology, Hyderabad（海得拉巴国际信息技术学院）；Center for Quantum Science and Technology, International Institute of Information Technology（国际信息技术学院量子科学与技术中心）
Multi-state imaginarity and coherence in qubit systems
School of Mathematics, South China University of Technology（华南理工大学数学学院）；Institut für Theoretische Physik, Universität Ulm（乌尔姆大学理论物理研究所）；INL – International Iberian Nanotechnology Laboratory（伊比利亚纳米技术国际实验室）；Centro de Física, Universidade do Minho（米尼奥大学物理中心）；School of Science, Hangzhou Dianzi University（杭州电子科技大学理学院）
Full characterization of informative subsets in Quantum Encrypted Cloning
Università degli Studi di Milano-Bicocca（米兰比可卡大学）；Università degli Studi di Milano（米兰大学）；Università Cattolica del Sacro Cuore（天主教神圣之心大学）；Institut National des Sciences Appliquées de Lyon（里昂国立应用科学学院）
