Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions

Details Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions

2007-08-30

arxiv.org/abs/0708.4114v2

J. Phys. A: Math. Theor. 40 (2007), 15099-15111

Physics

Quantum Physics

13 pages; accepted in J. Phys. A: Math. Theor

Scientific paper

10.1088/1751-8113/40/50/013

Mutually unbiased bases in Hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity. An alternative proof of existence of a maximal collection of N+1 mutually unbiased bases in Hilbert spaces of prime dimension N is given by exploiting the finite Heisenberg group (also called the Pauli group) and the action of SL(2,Z_N) on finite phase space Z_N x Z_N implemented by unitary operators in the Hilbert space. Crucial for the proof is that, for prime N, Z_N is also a finite field.

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