Joint product numerical range and geometry of reduced density matrices

作     者：Jianxin Chen Cheng Guo Zhengfeng Ji Yiu-Tung Poon Nengkun YU Bei Zeng Jie Zhou 

作者机构：Joint Center for Quantum Information and Computer Science University of Maryland College Park 20740 USA Institute for Advanced Study Tsinghua University Beijing 100084 China Centre for Quantum Computation ＆ Intelligent Systems School of Software Faculty of Engineering and Information Technology University of Technology Sydney Sydney 2007 Australia State Key Laboratory of Computer Science.Institute of Software Chinese Academy of Sciences Beijing 100084 China Department of Mathematics Iowa State University Ames 50011-2140 USA Institute for Quantum Computing University of Waterloo Waterloo N2L 3G1 Canada Department of Mathematics ＆ Statistics University of Guelph Guelph N1G 2 W1 Canada Perimeter Institute for Theoretical Physics Waterloo N2L 2Y5 Canada 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2017年第60卷第2期

页      面：9-17页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：supported by the Natural Sciences and Engineering Research Council of Canada,Canadian Institute for Advanced Research,Perimeter Institute for Theoretical Physics Research at Perimeter Institute was supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development&Innovation 

主　　题：reduced density matrices quantum tomography numerical range quantum information oloid ruled surface 

摘      要：The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection is convex in R3. The boundary of may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces： symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti＇s theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range II of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that a ruled surface emerges naturally when taking a convex hull of ∏. We show that, a ruled surface on sitting in ∏ has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of , with two boundary pieces of symmetry breaking origin separated by two gapless lines.