7 research outputs found
The Multiple-Access Channel with Entangled Transmitters
Communication over a classical multiple-access channel (MAC) with
entanglement resources is considered, whereby two transmitters share
entanglement resources a priori before communication begins. Leditzki 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
determine the capacity region for the general MAC with entangled transmitters,
and show that the previous result can be obtained as a special case.
Furthermore, 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
On the separation of correlation-assisted sum capacities of multiple access channels
The capacity of a channel characterizes the maximum rate at which information
can be transmitted through the channel asymptotically faithfully. For a channel
with multiple senders and a single receiver, computing its sum capacity is
possible in theory, but challenging in practice because of the nonconvex
optimization involved. In this work, we study the sum capacity of a family of
multiple access channels (MACs) obtained from nonlocal games. For any MAC in
this family, we obtain an upper bound on the sum rate that depends only on the
properties of the game when allowing assistance from an arbitrary set of
correlations between the senders. This approach can be used to prove
separations between sum capacities when the senders are allowed to share
different sets of correlations, such as classical, quantum or no-signalling
correlations. We also construct a specific nonlocal game to show that the
approach of bounding the sum capacity by relaxing the nonconvex optimization
can give arbitrarily loose bounds. Towards a potential solution to this
problem, we first prove a Lipschitz-like property for the mutual information.
Using a modification of existing algorithms for optimizing Lipschitz-continuous
functions, we then show that it is possible to compute the sum capacity of an
arbitrary two-sender MAC to a fixed additive precision in quasi-polynomial
time. We showcase our method by efficiently computing the sum capacity of a
family of two-sender MACs for which one of the input alphabets has size two.
Furthermore, we demonstrate with an example that our algorithm may compute the
sum capacity to a higher precision than using the convex relaxation.Comment: v2: 64 pages, 2 figures; updated conclusion and acknowledgements
sections, and added a referenc