xQIT Focus Area 2: Capacities and Coding for Quantum Communication
Channels
Team
Prof. Jeffrey Shapiro, Team Leader
Prof. Leonid Levitov
Prof. Seth Lloyd
Prof. Sanjoy Mitter
Prof. Peter Shor
Postdoctoral Fellow
Graduate Student
Visiting Scientists
Why it is important to solve the problem?
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.
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