PreprintarXiv licencearXiv
Two-copy distillability of one-copy-undistillable negative-partial-transpose states in every dimension
Abstract
Whether entanglement with a negative partial transpose (NPT) can be undistillable is a longstanding open problem. In the canonical family of DiVincenzo \textit{et al.}, the one-copy-undistillable region was conjectured to remain undistillable at all copy numbers. We refute this: in every dimension d≥3, one vertex of this region is two-copy distillable, via an explicit Schmidt-rank-two tight-frame witness. The separation persists on an open set, while other states in the same region are provably two-copy undistillable. Twirling our counterexample into Werner form makes it two-copy undistillable, so this standard reduction can erase finite-copy distillability.
Related
- Streaming the partial-transpose moment hierarchy with order-independent quantum memory
- Online Estimation of Partial Transpose Moments via Fast Classical Updates
- Many-body entanglement quantification in arbitrary states through a few partial-transpose moments
- Spectral bounds for the partial transpose
- A solution to 2-copy distillability of Werner states
BibTeX
@misc{tabia2026twocopy,
title = {{Two-copy distillability of one-copy-undistillable negative-partial-transpose states in every dimension}},
author = {Gelo Noel M. Tabia and Kai-Siang Chen and Min-Hsiu Hsieh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.08836},
eprint = {2608.08836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08836},
}
RIS
TY - UNPB
TI - Two-copy distillability of one-copy-undistillable negative-partial-transpose states in every dimension
AU - Gelo Noel M. Tabia
AU - Kai-Siang Chen
AU - Min-Hsiu Hsieh
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2608.08836
UR - https://arxiv.org/abs/2608.08836
AB - Whether entanglement with a negative partial transpose (NPT) can be undistillable is a longstanding open problem. In the canonical family of DiVincenzo \textit{et al.}, the one-copy-undistillable region was conjectured to remain undistillable at all copy numbers. We refute this: in every dimension d≥3, one vertex of this region is two-copy distillable, via an explicit Schmidt-rank-two tight-frame witness. The separation persists on an open set, while other states in the same region are provably two-copy undistillable. Twirling our counterexample into Werner form makes it two-copy undistillable, so this standard reduction can erase finite-copy distillability.
ER -