Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy

TL;DR

This paper proves a strong converse theorem for the classical capacity of entanglement-breaking and Hadamard quantum channels using sandwiched Renyi relative entropy, sharpening the understanding of communication limits.

Contribution

It establishes a universal strong converse for these channels by bounding success probability with sandwiched Renyi entropy and demonstrating its subadditivity, extending prior specific results.

Findings

Strong converse holds for all entanglement-breaking channels.

Strong converse holds for all Hadamard channels.

Results unify and extend previous covariant channel theorems.

Abstract

A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel. Along with a corresponding achievability statement for rates below the capacity, such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication. Here, we show that such a strong converse theorem holds for the classical capacity of all entanglement-breaking channels and all Hadamard channels (the complementary channels of the former). These results follow by bounding the success probability in terms of a "sandwiched" Renyi relative entropy, by showing that this quantity is subadditive for all entanglement-breaking and Hadamard channels, and by relating this quantity to the Holevo capacity. Prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results.