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 boundedsize 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.
How can we characterize different types of correlation between quantum systems? Since correlations cannot be generated locally, we take any real function of a multipartite state which cannot increase under local operations to measure a correlation. Correlation measures that can be expressed as an optimization of a linear combination of entropies are particularly useful, since they can often be interpreted operationally. We systematically study such optimized linear entropic functions, and by enforcing monotonicity under local processing we identify four cones of correlation measures for bipartite quantum states. This yields two new optimized measures of bipartite quantum correlation that are particularly simple, which have the additional property of being additive.
Recent developments have exposed close connections between quantum information and holography. In this paper, we explore the geometrical interpretations of the recently introduced Qcorrelation and R-correlation, EQ and ER. We find that EQ admits a natural geometric interpretation via the surface-state correspondence: it is a minimal mutual information between a surface region A and a cross-section of A's entanglement wedge with B. We note a strict trade-off between this minimal mutual information and the symmetric side-channel assisted distillable entanglement from the environment E to A, I ss (E A). We also show that the R-correlation, ER, coincides holographically with the entanglement wedge cross-section. This further elucidates the intricate relationship between entanglement, correlations, and geometry in holographic field theories. I. INTRODUCTIONInformation measures quantify the various types of information and disorder contained in the state of a quantum system. Familiar information measures such as the mutual information are built as linear combinations of entropies; others, such as the squashed entanglement [1], involve the optimization over additional auxiliary degrees of freedom.A particularly useful class of information measures, which we refer to as correlation measures, are those that are monotonically decreasing under local quantum operations. Such a monotonic measure captures properties of the state that individual parties cannot create on their own, and thus quantifies correlations between parties.The entanglement of purification is an especially interesting information measure [2]. It is defined as a minimization over purifications of the state ρ AB to |ψ AaBb of the entropy S(Aa),
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