LINEAR MAPS PRESERVING TENSOR PRODUCTS OF RANK-ONE HERMITIAN MATRICES

作者：Xu, Jinli^*; Zheng, Baodong; Fosner, Ajda

来源：Journal of the Australian Mathematical Society, 2015, 98(3): 407-428.

DOI：10.1017/S1446788714000603

• quantum information science
• linear preserver
• tensor product
• rank-one matrix
• Hermitian matrix

For a positive integer n >= 2, let M-n be the set of n x n complex matrices and H-n the set of Hermitian matrices in M-n. We characterize injective linear maps phi : H-m1... ml -> H-n satisfying @@@ rank(A(1) circle times . . . circle times A(l)) = 1 double right arrow rank(phi (A(1) circle times . . . circle times A(l))) = 1 @@@ for all A(k) epsilon H-mk, k = 1, . . . , l, where l; m(1), . . . , m(l) >= 2 are positive integers. The necessity of the injectivity assumption is shown. Moreover, the connection of the problem to quantum information science is mentioned.

• 出版日期2015-6
• 单位哈尔滨工业大学