A note on the Bloch representation of absolutely maximally entangled states
Bo Li, Shuhan Jiang, Shao-Ming Fei, and Xianqing Li-Jost
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Submission date: 28. Aug. 2017 (revised version: January 2018)
published in: Science in China : physics, mechanics and astronomy, 61 (2018) 4, art-no. 040321
DOI number (of the published article): 10.1007/s11433-017-9133-6
PACS-Numbers: 03.67.-a, 03.65.Ud, 03.65.Yz
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The absolutely maximally entangled (AME) states play key roles in quantum information processing. We provide an explicit expression of the generalized Bloch representation of AME states for general dimension d of individual subsystems and arbitrary number of partite n. Based on this analytic formula, we prove that the trace of the squared support for any given weight is given by the so-called hyper-geometric function and is irrelevant with the choices of the subsystems. The optimal point for the existence of AME states is obtained.