xQIT: Capacities and Coding for Quantum Communication Channels\n

xQIT: Capacities and Coding for Quantum Communication Channels
The ability to communicate is one of mankind’s most valuable and important abilities, and the growth of modern communication networks is one of today’s most enabling technologies. Simply stated, the world is "wired for comm," with its interconnected web of fiber optics, cellular wireless, and satellite communications linking people, computers, and a host of embedded processors in a myriad of ways that defy easy enumeration. Increasingly, technological and social progress hinges on the availability of high-quality communications.

Shannon’s theory for the capacity of classical communication channels was one of the most powerful and practical results in applied mathematics of the twentieth century. Shannon derived simple formulae for the amount of information that could be encoded, sent down noisy communication channels, and reliably decoded at the the far end. When it was published it turned conventional thinking -- which held that noise presented an unavoidable and impossible to defeat impediment to error-free communication -- upside down. Shannon taught us -- what is now so ingrained in our thinking as to be obvious— that with digital communication and appropriate error-control coding the presence of noise on a communication link restricts the maximum rate at which error-free communication can occur. This maximum rate, of course, is Shannon’s channel capacity. Because of the importance of its applications, Shannon’s theory has proven to be one of the most useful pieces of applied mathematics ever created. It represents a high point of applied mathematics in the twentieth century.

All communication channels, at bottom, are quantum mechanical. Existing fiberoptic communication channels, and initial demonstrations of satellite-based optical communications, are approaching performance limits set by quantum mechanics. Once again, these are called standard quantum limits, because these conventional communication systems were not designed to fully explore and exploit the possibilities offered by quantum physics. In fact, the ultimate limits on reliable classical information transmission over quantum channels are not understood, because the quantum version of Shannon’s theory is not yet fully established. Thus, despite recent advances (many by researchers at MIT) in deriving capacity bounds for quantum channels and in devising coding schemes for approaching ultimate communication-performance limits, the full capacity of the noisy quantum communication channel has yet to be determined.