Completely positive semidefinite rank

• Main Authors: Prakash, Anupam, Sikora, Jamie, Varvitsiotis, Antonios, Wei, Zhaohui
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2020
• Subjects: Science::Mathematics; Completely Positive Semidefinite Cone; CPSD-rank
• Online Access: https://hdl.handle.net/10356/139101
• Institution: Nanyang Technological University

An n× n matrix X is called completely positive semidefinite (cpsd) if there exist d× d Hermitian positive semidefinite matrices {Pi}i=1n (for some d≥ 1) such that Xij= Tr (PiPj) , for all i, j∈ { 1 , … , n}. The cpsd-rank of a cpsd matrix is the smallest d≥ 1 for which such a representation is possi...