Channels show unlimited gaps in information capacity in quantum systems
Unbounded Holevo additivity gaps in finite dimensions
Information Theory
Summary
Figuring out how much information can be sent through quantum channels is a key problem in quantum communication. This paper finds examples where sending information twice through certain quantum channels gives much more capacity than just twice sending once, with gaps that grow without limit. The authors build these channels using advanced mathematical techniques and show the difference can get very large even in finite-size systems. This challenges some expectations about how information capacity adds up in quantum settings.
What this means in practice
- •For quantum communication engineers: Design quantum communication protocols accounting for potentially unlimited capacity increases when using channels multiple times.
- •For quantum cryptography teams: Assess security models by considering channels with large nonlinear capacity behavior in multi-use scenarios.
A theory result. No direct application yet.
Authors
Jinzhao Wang
Abstract
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