Kirkman’s Schoolgirls and Quantum Spin Pairs: A 175 Year Long Thread Through Mathematics and Physics
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Abstract
Fifteen schoolgirls spread (5X3) across a week, a pair of qubits, 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. This will be an easily accessible pedagogical presentation, also to students, undergraduate and graduate.
Bio
A. Ravi. P. Rau is a Professor of Physics at Louisiana State University who conducts theoretical studies in atomic and molecular physics. He has held visiting faculty positions at Yale, the Raman Research Institute, Bangalore, India, the Tata Institute of Fundamental Research, Bombay, India, the Australian National University, Camberra, and the University of Freiberg, German. he was also a Visiting Fellow at the Joint Institute for Laboratory Astrophysics, Boulder, Co, in 1984. He is a Fellow of the American Physical Society and wa awarded the K. S. Krishman Gold Medal from the University of Delhi.
His recent interest is in the area of quantum information: studies of entanglement and other correlations such as quantum discord, their evolution under dissipative and decoherent processes and how they may be controlled, geometrical and symmetry studies of operators and states of N qubits and connections betweem the Lie and clifford algebras involved with topics in projective geometry and design theory.
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