Quantum capacity of the depolarizing and qubit Pauli channels

Determine the quantum capacity of qubit Pauli channels; even the depolarizing channel's zero-capacity threshold is only known to lie between 0.064956 and 1/12.

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1	{
2	"domain": "physics-astronomy",
3	"topics": [
4	"quantum-information",
5	"coding-theory"
6	],
7	"type": "proof",
8	"also": [
9	"construction"
10	],
11	"source": {
12	"key": "qiqcop",
13	"name": "QIQCOP Zoo",
14	"url": "https://qiqc-op.com/problem/op_43d4aca67bd52554/",
15	"id": "op_43d4aca67bd52554",
16	"curator": "Bikun Li, Qicheng Tang, Changhao Li, Chengkai Zhu, Minbo Gao, Zhong-Xia Shang, Bin Cheng and Naixu Guo",
17	"poser": "Bennett, DiVincenzo, Smolin and Wootters (1996) and DiVincenzo, Shor and Smolin (1998), implicitly",
18	"status": "unsolved",
19	"as_of": "2026-10-20",
20	"catalog": "0521c19bbd38"
21	},
22	"review": true,
23	"approval": "first-time"
24	}