Strong converse bounds on the classical identification capacity of the qubit depolarizing channel

TL;DR

This paper establishes strong converse bounds for the classical identification capacity of the qubit depolarizing channel, accurately reflecting the channel's noise level and matching achievable bounds under certain measurement constraints.

Contribution

It derives new strong converse bounds that vanish with increasing noise and proves the identification capacity equals the classical capacity under specific measurement conditions.

Findings

Converse bounds vanish as noise parameter p approaches 1.

In the setting of product measurements, the capacity equals the classical capacity.

Previous bounds remained positive even for fully noisy channels, which was unsatisfactory.

Abstract

A strong converse bound for the classical identification capacity of a quantum channel is an upper bound on the asymptotic identification rate of classical messages sent through the channel, such that, above this rate, the probability of an identification error necessarily converges to one. Converse bounds for identification are notoriously difficult to obtain for fully quantum channels. The only previously known converse bound, due to Atif, Pradhan and Winter [Int.~J.~Quantum Inf.~22(5):2440013, 2024], has the unsatisfactory feature of remaining strictly positive even for a completely noisy channel, for which identification is clearly impossible. We derive strong (and hence also weak) converse bounds, for the qubit depolarizing channel with noise parameter $p$, that vanish as $p\to 1$, thereby yielding the correct behavior in the completely noisy limit. Moreover, in the setting of simultaneous classical identification under the constraint of complete product measurements, our converse bound matches the corresponding achievability bound, and establishes that in this case the identification capacity equals the classical capacity of the channel.