Researchers present a concrete three-level (qutrit) quantum channel whose ability to send quantum data or private classical data is exactly zero. In the language of quantum information, the channel’s quantum capacity Q and private capacity P both vanish. These capacities measure how much quantum or private classical information can be sent reliably over many uses of a channel. Showing they are zero means no reliable quantum or private communication is possible through this channel, even with arbitrary coding across many uses.

The paper gives the channel in a simple formula. For a 3×3 input matrix X, the channel Λ maps X to ½X + 1/4(Tr(X) I − X^T), where Tr is the trace, I is the identity matrix, and X^T is the transpose. The authors prove that for every number n of channel uses, the one-shot optimized coherent information and the one-shot optimized private information of Λ⊗n are both zero. From that exact blockwise statement they conclude the asymptotic capacities P(Λ) and Q(Λ) are zero.

The proof does not follow the two standard reasons known to kill capacity. One standard reason is antidegradability: when the channel’s environment can simulate everything the receiver gets, then both capacities vanish. The other is the positive-partial-transpose (PPT) mechanism, tied to bound entanglement, which also forces zero quantum capacity. Instead the authors compare, in a precise information sense, how well the environment and the receiver can distinguish different inputs. They show that the environment’s output always dominates the receiver’s output in relative entropy — a measure of distinguishability — even when inputs are entangled with an arbitrary finite reference system and for every tensor power.

To get that comparison the authors build a mathematical certificate called a signed lift. This is a linear map that is adjoint-preserving but not necessarily positive. The failure of positivity is tightly controlled by a ‘‘defect’’ that admits an exact rank‑three completely positive (CP) factorization. Using that factorization together with established bridges between a Bogoliubov–Kubo–Mori (BKM) form and relative entropy, and with tensorization results for the relevant orders, they lift a single-use dominance statement to every blocklength and thus prove exact vanishing of the optimized coherent and private informations.