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Shanqi PANG Xiankui PENG Xiao ZHANG Ruining ZHANG Cuijiao YIN
Quantum combinatorial designs are gaining popularity in quantum information theory. Quantum Latin squares can be used to construct mutually unbiased maximally entangled bases and unitary error bases. Here we present a general method for constructing quantum Latin arrangements from irredundant orthogonal arrays. As an application of the method, many new quantum Latin arrangements are obtained. We also find a sufficient condition such that the improved quantum orthogonal arrays [10] are equivalent to quantum Latin arrangements. We further prove that an improved quantum orthogonal array can produce a quantum uniform state.
Shanqi PANG Ruining ZHANG Xiao ZHANG
In this work, we introduce notions of quantum frequency arrangements consisting of quantum frequency squares, cubes, hypercubes and a notion of orthogonality between them. We also propose a notion of quantum mixed orthogonal array (QMOA). By using irredundant mixed orthogonal array proposed by Goyeneche et al. we can obtain k-uniform states of heterogeneous systems from quantum frequency arrangements and QMOAs. Furthermore, some examples are presented to illustrate our method.