A B Klimov et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 283 doi:10.1088/1464-4266/7/9/008
A B Klimov1, L L Sánchez-Soto2 and H de Guise3
Show affiliationsWe develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased bases, which exist for dimensions that are powers of a prime. For a d-dimensional system (qudit) we explicitly construct d+1 classes of maximally commuting operators, each one consisting of d−1 operators. One of these classes consists of diagonal operators that represent amplitudes (or inversions). By finite Fourier transformation, it is mapped onto ladder operators that can be appropriately interpreted as phase variables. We discuss examples of qubits and qutrits, and show how these results generalize previous approaches.
03.65.Vf Phases: geometric; dynamic or topological
03.65.Yz Decoherence; open systems; quantum statistical methods
Issue 9 (September 2005)
Received 28 April 2005, accepted for publication 27 June 2005
Published 23 August 2005
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