Finite and Profinite Quantum Systems

1. Introduction
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2. Partial Orders and Pontryagin Duality
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3. The Ring




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4. Quantum Systems with Variables in




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5. Finite Geometries and Mutually Unbiased Bases
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6. Quantum Logic of Finite Quantum Systems
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7. Applications
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8. Galois Fields
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9. Quantum Systems with Variables in




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10.
p-adic Numbers and Profinite Groups
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11. A Quantum System with Positions in the Profinite Group




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12. A Quantum System with Positions in the Profinite Group




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Keywords: Physics, Quantum Physics, Quantum Computing, Quantum Optics, Discrete Mathematics, Mathematical Physics