Quantum Channel Capacities
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Abstract
In 1948, Shannon defined the notion of the capacity of a communication channel, and gave a formula for it. His paper essentially founded the field of information theory, and channel capacity is central in the theory and practice of information transmission. However, Shannon's formula does not apply to channels in which quantum effects are important. If the channel, the transmitter, and the receiver can all use quantum mechanics, we need a different formula. In fact, it turns out that there are several formulas for the capacity of a quantum channel, depending on whether you want to transmit classical information or quantum information, and which additional resources (e.g. feedback or entanglement) the receiver and sender are allowed to use. The lecture discusses these capacities of a quantum channel, focussing on the basics, but also mentions some recent developments.
Bio
Peter Shor is Morss Professor of Applied Mathematics since 2003, and Chair of the Applied Mathematics Committee since 2015. He received the B.A. in mathematics from Caltech in 1981, and the Ph.D. in applied mathematics from MIT in 1985, under the direction of Tom Leighton. Following a postdoctoral fellowship at MSRI, he joined AT&T. He was a member of its Research staff, 1986-2003. He joined the MIT faculty in applied mathematics as full professor in 2003. Professor Shor's research interests are in theoretical computer science: currently on algorithms, quantum computing, computational geometry and combinatorics. In 1998, Peter Shor received the Nevanlinna Prize and the International Quantum Communication Award. He also received the Dickson Prize in Science from Carnegie-Mellon in 1998. He was awarded the Gödel Prize of the ACM and a MacArthur Foundation Fellowship in 1999. He received the King Faisal International Prize in Science in 2002, and was named one of Caltech's Distinguished Alumni in 2007. He is a member of the National Academy of Science (2002), and fellow of the American Academy of Arts and Sciences (2011). In 2017, Professor Shor received the Dirac Medal of the International Centre for Theoretical Physics. He also received the 2017 IEEE Information Theory Society Paper Award, jointly with Charles Bennett, Igor Devetak, Aram Harrow, and Andreas Winter for the paper "The Quantum Reverse Shannon Theorem and Resource Tradeoffs for Simulating Quantum Channels" which appeared in the IEEE Transactions on Information Theory, vol. 60, no. 5, pp. 2926–2959, May 2014. In 2018, Peter received the IEEE Eric E. Sumner Award, for Outstanding Contributions to Communications Technology. He also received the 2018 Micius Quantum Prize in April 2019.
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