This paper considers basic properties of super-operator norms induced by Schatten p-norms. Such super-operator norms arise in various contexts in the study of quantum information. It is proved that for completely positive super-operators, the value of any such norm is achieved by a positive semidefinite input, answering a question recently posed by King and Ruskai. However, for any choice of p, there exists a super-operator that is the difference of two completely positive, trace-preserving super-operators such that the value of the super-operator norm is not even achieved on a Hermitian input operator. Also considered are the properties of the above norms for super-operators tensored with the identity super-operator.
Quantum Approximation of Normalized Schatten Norms and Applications to Learning
University of California（加利福尼亚大学）；Center for Quantum Science and Engineering, University of California, Los Angeles（加利福尼亚大学洛杉矶分校量子科学与工程中心）；California NanoSystems Institute（加州纳米系统研究所）；The Molecular Biology Institute, University of California（加利福尼亚大学分子生物学研究所）
Additivity and chain rules for quantum entropies via multi-index Schatten norms
Inria（法国国家信息与自动化研究所）；ENS Lyon（里昂高等师范学院）；UCBL（里昂第一大学）；LIP（计算机科学实验室）；Télécom Paris - LTCI（巴黎电信学院-通信与图像实验室）；Institut Polytechnique de Paris（巴黎理工学院）；Inria Paris（法国国家信息与自动化研究所巴黎分部）
Approximate pushforward designs and image bounds on approximations
Trinity College Dublin（都柏林三一学院）；Nanyang Technological University（南洋理工大学）；Jagiellonian University（雅盖隆大学）；Center for Theoretical Physics, Polish Academy of Sciences（波兰科学院理论物理中心）；Guangdong Technion–Israel Institute of Technology（广东以色列理工学院）
