The Quantum Multiple-Access Channel with Cribbing Encoders

TL;DR

This paper explores quantum multiple-access channels with cribbing encoders, introducing noisy cribbing models and deriving capacity regions, including for classical-quantum cases, highlighting the impact of entanglement and measurement on communication limits.

Contribution

It introduces a quantum MAC model with noisy cribbing, derives achievable regions, and establishes capacity bounds, extending classical concepts to quantum settings.

Findings

Achievable regions for causal and non-causal cribbing scenarios.

Regularized capacity characterization for robust cribbing.

Capacity region determination for classical-quantum MAC with perfect cribbing.

Abstract

Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1. Based on the no-cloning theorem, perfect cribbing is impossible. This leads to the introduction of a MAC model with noisy cribbing. In the causal and non-causal cribbing scenarios, Transmitter 2 performs the measurement before the input of Transmitter 1 is sent through the channel. Hence, Transmitter 2's cribbing may inflict a "state collapse" for Transmitter 1. Achievable regions are derived for each setting. Furthermore, a regularized capacity characterization is established for robust cribbing, i.e. when the cribbing system contains all the information of the channel input. Building on the analogy between the noisy cribbing model and the relay channel, a partial decode-forward region is derived for a quantum MAC with non-robust cribbing. For the classical-quantum MAC with cribbing encoders, the capacity region is determined with perfect cribbing of the classical input, and a cutset region is derived for noisy cribbing. In the special case of a classical-quantum MAC with a deterministic cribbing channel, the inner and outer bounds coincide.