An absolutely maximally entangled state of eight ququarts

Find a pure state of eight four-level systems whose every four-party marginal is maximally mixed, or prove that none exists.

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1	{
2	"domain": "physics-astronomy",
3	"topics": [
4	"quantum-information",
5	"coding-theory"
6	],
7	"type": "construction",
8	"also": [
9	"proof"
10	],
11	"source": {
12	"key": "qiqcop",
13	"name": "QIQCOP Zoo",
14	"url": "https://qiqc-op.com/problem/op_b08ad9d4371ed0cb/",
15	"id": "op_b08ad9d4371ed0cb",
16	"curator": "Bikun Li, Qicheng Tang, Changhao Li, Chengkai Zhu, Minbo Gao, Zhong-Xia Shang, Bin Cheng and Naixu Guo",
17	"poser": "Felix Huber (IQOQI Open Quantum Problems, problem 35)",
18	"status": "unsolved",
19	"as_of": "2026-10-20",
20	"catalog": "0521c19bbd38"
21	},
22	"review": true,
23	"approval": "first-time"
24	}