Universal random codes: capacity regions of the compound quantum multiple-access channel with one classical and one quantum sender

Abstract

We consider the compound memoryless quantum multiple-access channel (QMAC) with two sending terminals. In this model, the transmission is governed by the memoryless extensions of a completely positive and trace preserving map which can be any element of a prescribed set of possible maps. We study a communication scenario, where one of the senders aims for transmission of classical messages while the other sender sends quantum information. Combining powerful universal random coding results for classical and quantum information transmission over point-to-point channels, we establish universal codes for the mentioned two-sender task. Conversely, we prove that the two-dimensional rate region achievable with these codes is optimal. In consequence, we obtain a multi-letter characterization of the capacity region of each compound QMAC for the considered transmission task.

Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks

“…An equivalence statement between the strong subspace transmission and entanglement transmission has been proven in [3]. Recently in [12], an instance of the present classically enhanced codes was used for universal coding of multiple access quantum channels, where one of the senders shares classical messages with the receiver while the other sends quantum information. Theorem 12 does not make a positive statement about the structure of A r,CET in the case where A d,CET = {(0, 0)}.…”

“…The present paper develops solutions for different models of channel uncertainty that are unavoidable when implementing such integrated services in real-world communication. Following up on the results of [12], an interesting direction for future work is towards finding the solution to the arbitrarily varying model for multiple access and broadcast channels as a key step in development of quantum networks.…”