# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Quantum Channel Capacities," by Charles H. Bennett and Peter W. Shor. *Science*, 19 March 2004, pages 1784-1787.

In this article, researchers Bennett and Shor consider the progress that has been made in quantum information theory. They begin by providing an overview of classical information theory, defining entropy---which quantifies the amount of uncertainty in a source---and capacity, "the maximum rate at which a channel can carry information without spoiling it." They discuss the extension of these two concepts to quantum systems. But while the quantum extension of entropy is straightforward, the same cannot be said of capacity. For one thing, there are several ways to define the capacity of quantum channels. Then there's the role of "entanglement," which they discuss at length, and refer to here as "the strangest quantum phenomenon." They conclude that "although several important questions remain unanswered, and undoubtedly further phenomena remain to be discovered, it is fair to say that we now have a broadly accurate understanding of quantum information as the natural generalization of its classical forebear."

*--- Claudia Clark*