Classical capacity upper bound improved for quantum noise channels
A pretty-tight converse on the classical capacity of generalized amplitude-damping channels
Information Theory
Summary
Sending classical information over quantum channels is important but figuring out the maximum rate reliably achievable can be very challenging. The generalized amplitude-damping channel is a common noise model in quantum communication whose capacity remains unknown. The authors revisited an older mathematical limit on this capacity and created a new version that can be computed efficiently. Their new bound is close to the best known achievable rate and better than prior bounds over most parameters, helping understand the limits of communication through these channels.
What this means in practice
- •For quantum communication engineers: Design communication systems that account for noise properties when transmitting classical data over quantum hardware by using tighter upper capacity limits.
- •For quantum error correction teams: Utilize improved capacity bounds to better evaluate error-correcting code performance under realistic quantum noise channels.
Authors
Kun Fang
Abstract
The classical capacity of a quantum channel is the highest rate at which classical information can be transmitted with vanishing error. Although the capacities of many fundamental quantum channels have been established, the capacity of the generalized amplitude-damping channel remains an open problem in quantum Shannon theory. In this work, we revisit a converse bound introduced by Brandão et al. [Phys. Rev. Lett. 106, 230502 (2011)], which upper-bounds the classical capacity in terms of a correlation measure. For the generalized amplitude-damping channel, we derive a relaxation of this measure that makes the converse bound efficiently computable. Numerical comparisons demonstrate that our bound is pretty tight in general and nearly coincides with the Holevo information at nonzero temperatures, significantly improving upon existing bounds across the entire parameter range.