Summary form only given. This is a survey talk on the topic of quantum communication complexity. A full survey paper by the author is available in Foundations of Physics (G. Brassard, vol.33(11), p.1593-1616, 2003).
Quantum communications helps us to enhance the security and efficiency of communications and to deepen our understanding of quantum physics. Its rapid development in recent years has attracted the interest of researchers from diverse fields such as physics, mathematics, and computer science. We review the background and current state of quantum communications technology, with an emphasis on quantum key distribution, quantum random number generation, and a relatively hot topic: device independent protocols.
The last lecture course that Nobel Prize winner Richard Feynman gave to students at Caltech was not on physics but on computer science. The course in 1983 was an overview of standard and not-so-standard topics in computer science, all given in Feynman’s inimitable style. This talk will begin by giving an overview of Feynman’s long-time interest in computing - starting with his time at Los Alamos during the war through to his suggestion of simulating physics on a quantum computer at a ‘Physics of Computation Conference at MIT in 1981 and his acting as a consultant for the parallel computer company, Thinking Machines. The talk will conclude with a summary of Feynman’s long-term interest in the physical limits to computation and the exemplary way he could communicate complex ideas to all types of audience.
The ability (or inability) to represent or approximate Boolean functions by polynomials is a central concept in complexity theory, underlying interactive and probabilistically checkable proof systems, circuit lower bounds, quantum complexity theory, and more. In this book, the authors survey what is known about a particularly natural notion of approximation by polynomials, capturing pointwise approximation over This book covers recent progress on proving approximate degree lower and upper bounds and describes some applications of the new bounds to oracle separations, quantum query and communication complexity, and circuit complexity. The authors explain how several of these advances have been unlocked by a particularly simple and elegant technique, called dual block composition, for constructing solutions to this dual linear program. They also provide concise coverage of even more recent lower bound techniques based on a new complexity measure called spectral sensitivity. Finally, they show how explicit constructions of approximating polynomials have been inspired by quantum query algorithms. This book provides a comprehensive review of the foundational and recent developments of an important topic in both classical and quantum computing. The reader has a considerable body of knowledge condensed in an accessible form to quickly understand the principles and further their own research.