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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File it in the catalog (shoal-catalog 0521c19bbd38)

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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	+}