aiqbench takeQuantum Comms

This research refutes a longstanding conjecture regarding the distillability of entanglement states with negative partial transpose (NPT), demonstrating that certain one-copy-undistillable states become distillable when two copies are combined. The study provides explicit mathematical witnesses for this phenomenon across all dimensions $d \geq 3$, while also noting how standard twirling operations can erase this finite-copy distillability. These findings refine the theoretical boundaries of quantum entanglement manipulation and have direct implications for quantum communication protocols relying on specific state families.

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Two-copy distillability of one-copy-undistillable negative-partial-transpose states in every dimension

arXivOctober 6, 20261 min read

arXiv:2608.08836v2 Announce Type: replace 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 $d\geq3$, 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.

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 $d\geq3$, 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.

6+16 pages, 2 figures. Added exact rational two-copy-undistillability certificates for regions inside $BCG$ for $d=3,\ldots, 8$, plus further finite-copy and numerical analysis

arXiv:2608.08836 [quant-ph]

(or arXiv:2608.08836v2 [quant-ph] for this version)

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