The “quantum” Turán problem for operator systems
The “quantum” Turán problem for operator
systems
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运营商面临的“量子”图兰问题
DOI：
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发表时间：
2018
影响因子：
0.6
通讯作者：
N. Weaver
中科院分区：
文献类型：
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作者：
N. Weaver
设V是M_n（C）的包含单位矩阵的线性子空间，且在Hermite转置下稳定. V的“量子k-团”是M_n（C）中的秩为k的正交投影P，其中dim（PVP）= k^2，而“量子k-反团”是秩为k的正交投影，其中dim（PVP）= 1。我们给出了V的最大维数的上界和下界，这将确保量子k-反团的存在，以及V的最小维数，这将确保量子k-团的存在。
Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under Hermitian transpose. A "quantum k-clique" for V is a rank k orthogonal projection P in M_n(C) for which dim(PVP) = k^2, and a "quantum k-anticlique" is a rank k orthogonal projection for which dim(PVP) = 1. We give upper and lower bounds both for the largest dimension of V which would ensure the existence of a quantum k-anticlique, and for the smallest dimension of V which would ensure the existence of a quantum k-clique.