🤖 AI Summary
This study investigates the fundamental limits of classical identification over quantum channels, with a focus on the relationship between identification capacity and transmission capacity in the presence of entanglement assistance. By integrating Hayden–Winter quantum identification codes, the entanglement-assisted communication model, and an analysis of the transpose depolarizing channel, the work establishes—for the first time—that the entanglement-assisted transmission capacity serves as a strong converse upper bound on the identification capacity. The main contributions include precisely characterizing the identification capacity as achieving this bound in the low-noise regime, constructing an explicit family of channels for which the identification capacity is strictly smaller than the bound in general, and uncovering the first known instance of strict superadditivity of identification capacity.
📝 Abstract
Classical identification via a noisy channel is a communication task in which the receiver is not required to reconstruct the full transmitted message, but only to decide whether it coincides with a message of interest. This relaxation allows the number of identifiable messages to grow doubly exponentially with the blocklength. For quantum channels, the resulting (doubly exponential) identification capacity $C_{\mathrm{ID}}$ can strictly exceed the ordinary (exponential) transmission capacity $C$.
In this paper, we prove that the entanglement-assisted transmission capacity $C_E$ is a strong converse bound for this task: $C_{\mathrm{ID}}\leq C_E$. For sufficiently low-noise channels, this bound can also be achieved via the Hayden-Winter (quantum) identification + fingerprinting codes. This yields an exact characterization $C_{\mathrm{ID}}=C_E$ of identification capacity for such channels. However, for general channels, we prove that this upper bound can be strict. We exhibit an explicit family of transpose-depolarizing channels for which $C_{\mathrm{ID}}<C_E$. As a consequence, we also obtain the first example of strict superadditivity of the identification capacity $C_{\mathrm{ID}}$.