Quantum-optical states in finite-dimensional Hilbert space. I. General formalism

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dc.creatorMiranowicz, Adam
dc.creatorLeonski, Wieslaw
dc.creatorImoto, Nobuyuki
dc.date2001-08-16
dc.date2001-10-19
dc.date.accessioned2026-07-07T06:02:35Z
dc.date.available2026-07-07T06:02:35Z
dc.descriptionThe interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation, and measurement techniques, in particular, by the development of the discrete quantum-state tomography. In the first part of our review we present two essentially different approaches to define harmonic oscillator states in the finite-dimensional Hilbert spaces. One of them is related to the truncation scheme of Pegg, Phillips and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] -- the so-called quantum scissors device. The second method corresponds to the truncation scheme of Leoński and Tanaś [Phys. Rev. A 49, R20 (1994)]. We propose some new definitions of the states related to these truncation schemes and find their explicit forms in the Fock representation. We discuss finite-dimensional generalizations of coherent states, phase coherent states, displaced number states, Schrödinger cats, and squeezed vacuum. We show some intriguing properties of the states with the help of the discrete Wigner function.
dc.description38 pages, 10 figures, the final version
dc.identifierhttps://arxiv.org/abs/quant-ph/0108080
dc.identifierhttp://arxiv.org/abs/quant-ph/0108080
dc.identifier"Modern Nonlinear Optics", ed. M. W. Evans, Advances in Chemical Physics, vol. 119 (I) (Wiley, New York, 2001) pp. 155-193
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/89655
dc.subjectQuantum Physics
dc.titleQuantum-optical states in finite-dimensional Hilbert space. I. General formalism
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