Simultaneous identification capacity of the qubit depolarizing channel without product-measurement restriction

Determine the simultaneous classical identification capacity of the qubit depolarizing channel under unrestricted decoding measurements (i.e., without imposing the complete product measurement constraint); establish whether this capacity equals the classical capacity C(N_p)=1−h(p/2); and ascertain whether entangled measurements can strictly improve identification rates over product measurements, including whether the capacity is achievable with product-state encodings and complete product measurements as in message transmission.

Background

The paper proves a matching achievability/converse for simultaneous identification over the qubit depolarizing channel when the decoder is restricted to complete product measurements, showing the capacity equals the classical capacity 1−h(p/2).

The authors highlight that this conclusion relies crucially on the product-measurement restriction and a reduction to a classical binary symmetric channel; for general (possibly entangled) measurements, such a reduction seems unavailable.

They note that in message transmission, King showed the depolarizing channel’s capacity is achieved with product-state inputs and product measurements, and ask whether an analogous statement holds for identification. They observe that even for two channel uses, while Bell measurements do not help, some partially/asymmetrically entangled measurements yield output distributions outside those of complete product measurements, leaving open whether entanglement can help.