Curator's Take
AI Commentary
This article demonstrates that even for modest‑size quantum channels the Holevo quantity can exhibit arbitrarily large superadditivity when two uses are combined, overturning the long‑standing intuition that additivity gaps should be bounded in finite dimensions. By constructing explicit families of mixed‑unitary channels with a linear gap in output qubits and only quadratic growth in input size, the work extends recent random‑matrix and free‑probability results into concrete, hardware‑relevant settings. The finding reshapes how we think about classical capacity limits for realistic devices, reminding engineers that multi‑use coding strategies may unlock far more information than single‑shot analyses suggest—though the constructions remain highly structured and not yet directly implementable.
— Mark Eatherly
Summary
We establish unbounded two-use Holevo additivity gaps in finite dimensions. For each sufficiently large fixed integer $K$ and all sufficiently large $n$, we construct channels $T_n$ with output dimension $K^n$, input dimension $\exp(Θ_K(n^2))$, and \[ χ(T_n^{\otimes2})-2χ(T_n) \ge n\left[\frac{\log_2K}{K}-2\log_2(1+9/K)\right]-O(1/n). \] The gap is linear in output qubits, with an explicit quadratic input-qubit cost and an explicit threshold on $n$. We also obtain channels whose single-use Holevo quantity tends to zero while their two-use Holevo information, and hence classical capacity, diverges. The channels arise from structured tensor products of the complementary mixed-unitary channels used in Collins's free-probabilistic proof. We establish minimum-output-entropy gaps by combining Collins--Youn's product-group Haagerup inequality with Bordenave--Collins's quantitative strong-convergence estimates