The Aaronson–Ambainis conjecture

Show that every bounded low-degree polynomial on the Boolean cube with non-negligible variance has a variable of polynomially large influence.

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1	{
2	"domain": "physics-astronomy",
3	"topics": [
4	"quantum-information",
5	"algorithms-complexity"
6	],
7	"type": "proof",
8	"source": {
9	"key": "qiqcop",
10	"name": "QIQCOP Zoo",
11	"url": "https://qiqc-op.com/problem/op_a11fdfadc84e4379/",
12	"id": "op_a11fdfadc84e4379",
13	"curator": "Bikun Li, Qicheng Tang, Changhao Li, Chengkai Zhu, Minbo Gao, Zhong-Xia Shang, Bin Cheng and Naixu Guo",
14	"poser": "Scott Aaronson and Andris Ambainis",
15	"status": "unsolved",
16	"as_of": "2026-10-20",
17	"catalog": "0521c19bbd38"
18	},
19	"review": true,
20	"approval": "first-time"
21	}