Fig. 2: Schematic of a general EA-MAC communication protocol.
From: Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels
The EA sources \(\hat{\phi }\) of the s senders are in a product state of Eq. (1). The s senders apply independent encoding modeled by quantum operations, i.e., sender k applies \({{\mathcal{E}}}_{{m}_{k}}\) on the signal state given the message mk. Denoting the entire message as m = m1 ⋯ ms, the encoded signal-idler is then in a state \({\hat{\sigma }}^{m}\). The senders’ encoded quantum systems A = A1 ⋯ As are sent through the MAC \({\mathcal{N}}\), leading to the output system B. The receiver applies the quantum operation \({\mathcal{D}}\) to decode the information from the joint state \({\hat{\beta }}^{m}\) of the output system B and the pre-shared reference systems \(A^{\prime} =A_1^{\prime} \cdots A_s^{\prime}\). We define Mk as the codeword space of each message mk, M as the overall codeword space of message m, and \({M}^{\prime}\) as the decoded codeword space. To facilitate the analysis, we denote the overall state \(\hat{{{\Xi }}}\) (Eq. (14)) over systems \(MA{A}^{\prime}\) right before the channel and the overall state \(\hat{\omega }\) (Eq. (15)) over systems \(MB{A}^{\prime}\) right before the decoding.
