We study the construction of mutually unbiased bases in Hilbert space for composite dimensions d which are not prime powers.We explore the results for composite dimensions which are true for prime power dimensions.We ...We study the construction of mutually unbiased bases in Hilbert space for composite dimensions d which are not prime powers.We explore the results for composite dimensions which are true for prime power dimensions.We then provide a method for selecting mutually unbiased vectors from the eigenvectors of generalized Pauli matrices to construct mutually unbiased bases.In particular,we present four mutually unbiased bases in C^(15).展开更多
This paper gives a definition of the Industrial Internet and expounds on the academic connotation of the future Industrial Internet.From this foundation,we outline the development and current status of the Industrial ...This paper gives a definition of the Industrial Internet and expounds on the academic connotation of the future Industrial Internet.From this foundation,we outline the development and current status of the Industrial Internet in China and globally.Moreover,we detail the avant-garde paradigms encompassed within the National Natural Science Foundation of China(NSFC)’s“Future Industrial Internet Fundamental Theory and Key Technologies”research plan and its corresponding management strategies.This research initiative endeavors to enhance interdisciplinary collaborations,aiming for a synergistic alignment of industry,academia,research,and practical implementations.The primary focus of the research plan is on the pivotal scientific challenges inherent to the future industrial internet.It is poised to traverse the“first mile”,encompassing foundational research and pioneering innovations specific to the industrial internet,and seamlessly bridges to the“last mile”,ensuring the effective commercialization of scientific and technological breakthroughs into tangible industrial market applications.The anticipated contributions from this initiative are projected to solidify both the theoretical and practical scaffolding essential for the cultivation of a globally competitive industrial internet infrastructure in China.展开更多
基金Project supported by Zhoukou Normal University,ChinaHigh Level Talents Research Start Funding Project (Grant No.ZKNUC2022010)+2 种基金Key Scientific Research Project of Henan Province (Grant No.22B110022)Key Research and Development Project of Guangdong Province (Grant No.2020B0303300001)the Guangdong Basic and Applied Basic Research Foundation (Grant No.2020B1515310016)。
文摘We study the construction of mutually unbiased bases in Hilbert space for composite dimensions d which are not prime powers.We explore the results for composite dimensions which are true for prime power dimensions.We then provide a method for selecting mutually unbiased vectors from the eigenvectors of generalized Pauli matrices to construct mutually unbiased bases.In particular,we present four mutually unbiased bases in C^(15).
文摘This paper gives a definition of the Industrial Internet and expounds on the academic connotation of the future Industrial Internet.From this foundation,we outline the development and current status of the Industrial Internet in China and globally.Moreover,we detail the avant-garde paradigms encompassed within the National Natural Science Foundation of China(NSFC)’s“Future Industrial Internet Fundamental Theory and Key Technologies”research plan and its corresponding management strategies.This research initiative endeavors to enhance interdisciplinary collaborations,aiming for a synergistic alignment of industry,academia,research,and practical implementations.The primary focus of the research plan is on the pivotal scientific challenges inherent to the future industrial internet.It is poised to traverse the“first mile”,encompassing foundational research and pioneering innovations specific to the industrial internet,and seamlessly bridges to the“last mile”,ensuring the effective commercialization of scientific and technological breakthroughs into tangible industrial market applications.The anticipated contributions from this initiative are projected to solidify both the theoretical and practical scaffolding essential for the cultivation of a globally competitive industrial internet infrastructure in China.
