Arithmetic, mutually unbiased bases and complementary observables

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3271045· OSTI ID:21335916

Sheppeard, M D ^[1]

---

1. Oxford University Computing Laboratory, Wolfson Building, Parks Rd., Oxford OX1 3QD (United Kingdom)

Complementary observables in quantum mechanics may be viewed as Frobenius structures in a dagger monoidal category, such as the category of finite dimensional Hilbert spaces over the complex numbers. On the other hand, their properties crucially depend on the discrete Fourier transform and its associated quantum torus, requiring only the finite fields that underlie mutually unbiased bases. In axiomatic topos theory, the complex numbers are difficult to describe and should not be invoked unnecessarily. This paper surveys some fundamentals of quantum arithmetic using finite field complementary observables, with a view considering more general axiom systems.

• OSTI ID: 21335916
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 2; Other Information: DOI: 10.1063/1.3271045; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPLEX MANIFOLDS
FOURIER TRANSFORMATION
HILBERT SPACE
QUANTUM MECHANICS