NPT bound entanglement: does undistillability imply PPT?

Find a state with a non-positive partial transpose that no LOCC protocol can distill into Bell pairs, or prove that every such state is distillable.

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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_74c4ffb5b042baf2/",
11	"id": "op_74c4ffb5b042baf2",
12	"curator": "Bikun Li, Qicheng Tang, Changhao Li, Chengkai Zhu, Minbo Gao, Zhong-Xia Shang, Bin Cheng and Naixu Guo",
13	"poser": "DiVincenzo, Shor, Smolin, Terhal and Thapliyal; Dür, Cirac, Lewenstein and Bruß (2000)",
14	"status": "unsolved",
15	"as_of": "2026-10-20",
16	"catalog": "0521c19bbd38"
17	}
18	}