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Open Quantum Systems Decoherence
Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions
arXiv
Authors: P. Sulc, J. Tolar
Year
2007
Paper ID
49215
Status
Preprint
Abstract Read
~2 min
Abstract Words
92
Citations
N/A
Abstract
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 SL2,ZN 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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- This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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- Mutually unbiased bases in Hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity.
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