Equivalence of Local Complementation and Euler Decomposition in the Qutrit ZX-calculus

Xiaoyan Gong; Quanlong Wang

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arXiv · 1704.05955

Equivalence of Local Complementation and Euler Decomposition in the Qutrit ZX-calculus

Xiaoyan Gong·Quanlong Wang

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Abstract

In this paper, we give a modified version of the qutrit ZX-calculus, by which we represent qutrit graph states as diagrams and prove that the qutrit version of local complementation property is true if and only if the qutrit Hadamard gate $H$ has an Euler decomposition into $4\pi/3$-green and red rotations. This paves the way for studying the completeness of qutrit ZX-calculus for qutrit stabilizer quantum mechanics.

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Xiaoyan Gong, Quanlong Wang. 2017-04-19. Equivalence of Local Complementation and Euler Decomposition in the Qutrit ZX-calculus. https://arxiv.org/abs/1704.05955

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