The Multiple-Access Channel with Entangled Transmitters

TL;DR

This work analyzes a two-user classical MAC with pre-shared entanglement between transmitters and derives inner and outer bounds, plus a regularized capacity characterization, for the entanglement-assisted MAC. It shows that entanglement can strictly enlarge the capacity region beyond what is possible with classical correlation, while the error criterion does not alter the region when entanglement is present. The paper also extends to settings where transmitters can conference over classical or quantum links, leveraging superdense coding to double quantum conferencing rates and obtaining corresponding achievable regions. Through pseudo-telepathy examples (magic square and Slofstra–Vidick games), it demonstrates concrete separations between entanglement-assisted and classical-conference capacities. Purification, cardinality bounds, and detailed achievability/converse proofs underpin the results, and the discussion highlights unbounded entanglement dimensions and open questions for future research in quantum-enhanced MACs and 6G networking contexts.

Abstract

Communication over a classical multiple-access channel (MAC) with entanglement resources is considered, whereby two transmitters share entanglement resources a priori before communication begins. Leditzky et al. (2020) presented an example of a classical MAC, defined in terms of a pseudo telepathy game, such that the sum rate with entangled transmitters is strictly higher than the best achievable sum rate without such resources. Here, we establish inner and outer bounds on the capacity region for the general MAC with entangled transmitters, and show that the previous result can be obtained as a special case. It has long been known that the capacity region of the classical MAC under a message-average error criterion can be strictly larger than with a maximal error criterion (Dueck, 1978). We observe that given entanglement resources, the regions coincide. Furthermore, we address the combined setting of entanglement resources and conferencing, where the transmitters can also communicate with each other over rate-limited links. Using superdense coding, entanglement can double the conferencing rate.

Figures (5)

• Figure 1: The classical multiple-access channel $P_{Y|X_1,X_2}$ with pre-shared entanglement resources between the transmitters. The entanglement resources (quantum systems) of Transmitter 1 and Transmitter 2 are marked in red and blue, respectively.
• Figure 2: The classical multiple-access channel $P_{Y|X_1,X_2}$ with pre-shared entanglement resources and classical conferencing between the transmitters. The entanglement resources of Transmitter 1 and Transmitter 2 are marked in blue and red, respectively. The conferencing links are indicated by double-line arrows.
• Figure 3: The classical multiple-access channel $P_{Y|X_1,X_2}$ with pre-shared entanglement resources and quantum conferencing between the transmitters. The quantum systems of Transmitter 1 and Transmitter 2 are marked in blue and red, respectively.
• Figure 4: Rate bounds for the magic-square multiple-access channel $P_{Y|X_1,X_2}$ in Example \ref{['Example:Magic_Square']}. The gray triangle indicates the outer bound for the capacity region $\mathcal{C}_{\text{CRT}}(P_{Y|X_1,X_2})$, with classical CR between the transmitters. The green square is the capacity region $\mathcal{C}_{\text{ET}}(P_{Y|X_1,X_2})$, with entangled transmitters. The red area represents rate pairs that can be achieved with entanglement, but cannot be achieved with classical CR.
• Figure 5: Achievable rate regions for the magic-square multiple-access channel $P_{Y|X_1,X_2}$ with entangled transmitters and, either classical or quantum, conferencing, as in Example \ref{['Example:Magic_Square']}. The inner square indicates the capacity region $\mathcal{C}_{\text{ET}}(P_{Y|X_1,X_2})$ with entangled transmitters. The pentagon below the blue dashed line is an achievable region for the MAC with entangled transmitters and classical conferencing, for $C_{12}=C_{21}=0.5$ (see \ref{['eq:Cet_Magic_C']}). The pentagon below the red solid line is achievable when the conferencing links are quantum as well, for $Q_{12}=Q_{21}=0.5$ (see \ref{['eq:Cet_Magic_Q']}).

Theorems & Definitions (26)

• Definition 1
• Remark 1
• Theorem 1: see also Cai:14p
• Remark 2
• Definition 2
• Remark 3
• Definition 3
• Definition 4
• Remark 4
• Remark 5