Communication networks have multiple users, each sending and receiving messages. A multiple access channel (MAC) models multiple senders transmitting to a single receiver, such as the uplink from many mobile phones to a single base station. The optimal performance of a MAC is quantified by a capacity region of simultaneously achievable communication rates. We study the two-sender classical MAC, the simplest and best-understood network, and find a surprising richness in both a classical and quantum context. First, we find that quantum entanglement shared between senders can substantially boost the capacity of a classical MAC. Second, we find that optimal performance of a MAC with bounded-size inputs may require unbounded amounts of entanglement. Third, determining whether a perfect communication rate is achievable using finite-dimensional entanglement is undecidable. Finally, we show that evaluating the capacity region of a two-sender classical MAC is in fact NP-hard.
Communication networks have multiple users, each sending and receiving messages. A multiple access channel (MAC) models multiple senders transmitting to a single receiver, such as the uplink from many mobile phones to a single base station. The optimal performance of a MAC is quantified by a capacity region of simultaneously achievable communication rates. We study the two-sender classical MAC, the simplest and best-understood network, and find a surprising richness in both a classical and quantum context. First, we find that quantum entanglement shared between senders can substantially boost the capacity of a classical MAC. Second, we find that optimal performance of a MAC with bounded-size inputs may require unbounded amounts of entanglement. Third, determining whether a perfect communication rate is achievable using finite-dimensional entanglement is undecidable. Finally, we show that evaluating the capacity region of a two-sender classical MAC is in fact NP-hard.
Communication over a classical multiple-access channel (MAC) with quantum entanglement resources is considered, whereby two transmitters share entanglement resources a priori. Leditzky et al. (2020) presented an example, 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.
A multiple access channel (MAC) consists of multiple senders simultaneously transmitting their messages to a single receiver. For the classical-quantum case (CQ MAC), achievable rates are known assuming that all the messages are decoded, a common assumption in quantum network design. However, such a conventional design approach ignores the global network structure, i.e., the network topology. When a CQ MAC is given as a part of quantum network communication, this work shows that computation properties can be used to boost communication speeds with code design dependent on the network topology. We quantify achievable quantum communication rates of codes with the computation property for a two-sender CQ MAC. When the two-sender CQ MAC is a boson coherent channel with binary discrete modulation, we show that it achieves the maximum possible communication rate (the single-user capacity), which cannot be achieved with conventional design. Further, such a rate can be achieved by different detection methods: quantum (with and without quantum memory), on-off photon counting, and homodyne (each at different photon power). Finally, we describe two practical applications, one of which cryptographic.
Abstract We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels (MACs) with an arbitrary number of senders. As an example, we consider the bosonic thermal-loss MAC and solve the one-shot capacity region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA capacity region is strictly larger than the capacity region without entanglement-assistance. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. Four practical receiver designs, based on optical parametric amplifiers, are given and analyzed. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rates. Our work provides a unique and practical network communication scenario where entanglement can be beneficial.
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.
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.
We address the problem of coding for classical multiple-access channels (MACs) with the assistance of non-signaling correlations between parties. It is well-known that non-signaling assistance does not change the capacity of classical point-to-point channels. However, it was recently observed that one can construct MACs from two-player nonlocal games while relating the winning probability of the game to the capacity of the MAC. By considering games for which entanglement (a special kind of non-signaling correlation) increases the winning probability (e.g., the Magic Square game), this shows that for some specific kinds of channels, entanglement between the senders can increase the capacity. In this work, we make several contributions towards understanding the capacity region for MACs with the assistance of non-signaling correlations between the parties. We develop a linear program computing the optimal success probability for coding overncopies of a MACWwith size growing polynomially inn. Solving this linear program allows us to achieve inner bounds for MACs. Applying this method to the binary adder channel, we show that using non-signaling assistance, the sum-rate4log2(72)≃1.5425can be reached even with zero error, which beats the maximum sum-rate capacity of 1.5 in the unassisted case. For noisy channels, where the zero-error non-signaling assisted capacity region is trivial, we can use concatenated codes to obtain achievable points in the capacity region. Applied to a noisy version of the binary adder channel, we show that non-signaling assistance still improves the sum-rate capacity. Complementing these achievability results, we give an outer bound on the non-signaling assisted capacity region that has the same expression as the unassisted region except that the channel inputs are not required to be independent. Finally, we show that the capacity region with non-signaling assistance shared only between each sender and the receiver independently is the same as without assistance.