Qubit symmetries, combinatorial designs, and a rainbow of four basic colors: Common Patterns
A recreational puzzle posed 175 years ago of 15 schoolgirls to walk three abreast to school for seven days of the week so that no girl sees a friend repeated in her row has links to many areas of mathematics: combinatorics, finite projective geometries, design and coding theory, etc. A link can also be made to states and operators of two qubits in today's quantum information, those Lie algebras and groups also providing a systematic way to get the required arrangements of the girls. These patterns can be further linked to four-color vision and analogs in acoustics. They may be useful for
manipulating states and operators of a pair of qubits, with generalization also to multiple qubits. The Bloch Sphere is a well-known and very useful geometrical picture of a single qubit. Similar geometries and pictures will be discussed for two or more qubits. This will be an easily accessible pedagogical presentation, also to students, undergraduate and graduate.
Bio: A. Ravi R. Rau is a Professor of Physics at Louisiana State University. He is a theoretical physicist, working mostly in the sub-area of atomic physics but broadly interested in all physics. A recurring theme of his research has been the dynamics of a particle when two (or more) fields influence its motion equally strongly. He also researches mathematical physics, especially the development of variational principles and solving time-dependent operator equations. In recent years, his work is in the sub-area of physics called quantum information, where quantum correlations like entanglement between entities such as quantum spins are studied for possible application in computation and cryptography. Dr. Rau is particularly interested in exploiting symmetries in such systems, developing mathematical procedures and geometrical pictures.
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