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Finite and Profinite Quantum Systems (Hardcover, 1st ed. 2017)
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Finite and Profinite Quantum Systems (Hardcover, 1st ed. 2017)
Series: Quantum Science and Technology
Expected to ship within 12 - 17 working days
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This monograph provides an introduction to finite quantum systems,
a field at the interface between quantum information and number
theory, with applications in quantum computation and condensed
matter physics. The first major part of this monograph studies the
so-called `qubits' and `qudits', systems with periodic finite
lattice as position space. It also discusses the so-called mutually
unbiased bases, which have applications in quantum information and
quantum cryptography. Quantum logic and its applications to quantum
gates is also studied. The second part studies finite quantum
systems, where the position takes values in a Galois field. This
combines quantum mechanics with Galois theory. The third part
extends the discussion to quantum systems with variables in
profinite groups, considering the limit where the dimension of the
system becomes very large. It uses the concepts of inverse and
direct limit and studies quantum mechanics on p-adic numbers.
Applications of the formalism include quantum optics and quantum
computing, two-dimensional electron systems in magnetic fields and
the magnetic translation group, the quantum Hall effect, other
areas in condensed matter physics, and Fast Fourier Transforms. The
monograph combines ideas from quantum mechanics with discrete
mathematics, algebra, and number theory. It is suitable for
graduate students and researchers in quantum physics, mathematics
and computer science.
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