Copy-dependent distillability in the DiVincenzo state family
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Are the states at canonical point C of the DiVincenzo family undistillable for every number of copies? The question is distinct from one-copy undistillability and is considered in every local dimension d≥3.
Why it matters and what counts as progress
Why it matters: Two-copy distillation can invalidate an all-copy undistillability proposal despite a valid one-copy obstruction.
What counts as progress: Construct a finite-copy Schmidt-rank-two distillation witness or prove undistillability for additional copy numbers.
How the problem developed
- 2000 · Conjecture [1]
DiVincenzo, Shor, Smolin, Terhal and Thapliyal Introduced the canonical two-parameter NPT state family, identified a one-copy-undistillable region, and conjectured it may remain undistillable at all copy numbers.
- 2022 · Open problem [1]
Horodecki, Rudnicki and Życzkowski Listed two-copy distillability of a two-ququart Werner state among open problems in quantum information.
- 9 Aug 2026 · Partial result [1]
Gelo Noel M. Tabia, Kai-Siang Chen and Min-Hsiu Hsieh with GPT-5.6 Thinking assistance Proved one vertex of the DiVincenzo one-copy-undistillable region is two-copy distillable for every d≥3, refuting the all-copy conjecture there.
AI contribution
Two-copy distillability of one-copy-undistillable negative-partial-transpose states in every dimension
At canonical point C of the DiVincenzo family, an explicit Schmidt-rank-two tight-frame witness proves one-copy undistillability but two-copy distillability for every local dimension d≥3.
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