Mutually-orthogonal unitary and orthogonal matrices

• URL: http://arxiv.org/abs/2309.11128v1
• Date: Wed, 20 Sep 2023 08:20:57 GMT
• Title: Mutually-orthogonal unitary and orthogonal matrices
• Authors: Zhiwei Song, Lin Chen and Saiqi Liu
• Abstract summary: We show that the minimum and maximum numbers of an unextendible maximally entangled bases within a real two-qutrit system are three and four, respectively. As an application in quantum information theory, we show that the minimum and maximum numbers of an unextendible maximally entangled bases within a real two-qutrit system are three and four, respectively.
• Score: 6.9607365816307
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the concept of n-OU and n-OO matrix sets, a collection of n mutually-orthogonal unitary and real orthogonal matrices under Hilbert-Schmidt inner product. We give a detailed characterization of order-three n-OO matrix sets under orthogonal equivalence. As an application in quantum information theory, we show that the minimum and maximum numbers of an unextendible maximally entangled bases within a real two-qutrit system are three and four, respectively. Further, we propose a new matrix decomposition approach, defining an n-OU (resp. n-OO) decomposition for a matrix as a linear combination of n matrices from an n-OU (resp. n-OO) matrix set. We show that any order-d matrix has a d-OU decomposition. As a contrast, we provide criteria for an order-three real matrix to possess an n-OO decomposition.

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