Separability from spectrum

Characterize the spectra that force every bipartite state with those eigenvalues to be separable, and decide whether a PPT test suffices.

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1	{
2	"domain": "physics-astronomy",
3	"topics": [
4	"quantum-information"
5	],
6	"type": "proof",
7	"source": {
8	"key": "qiqcop",
9	"name": "QIQCOP Zoo",
10	"url": "https://qiqc-op.com/problem/op_b063bdae4363cda8/",
11	"id": "op_b063bdae4363cda8",
12	"curator": "Bikun Li, Qicheng Tang, Changhao Li, Chengkai Zhu, Minbo Gao, Zhong-Xia Shang, Bin Cheng and Naixu Guo",
13	"poser": "Emanuel Knill (2003)",
14	"status": "unsolved",
15	"as_of": "2026-10-20",
16	"catalog": "0521c19bbd38"
17	},
18	"review": true,
19	"approval": "first-time"
20	}