dorsal/arxiv
View SchemaQuantum-optical states in finite-dimensional Hilbert space. I. General formalism
| Authors | Adam Miranowicz, Wieslaw Leonski, Nobuyuki Imoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108080 |
| URL | https://arxiv.org/abs/quant-ph/0108080 |
| Journal | "Modern Nonlinear Optics", ed. M. W. Evans, Advances in Chemical Physics, vol. 119 (I) (Wiley, New York, 2001) pp. 155-193 |
Abstract
The 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 Leo\'nski and Tana\'s [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, Schr\"odinger cats, and squeezed vacuum. We show some intriguing properties of the states with the help of the discrete Wigner function.
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"abstract": "The interest in quantum-optical states confined in finite-dimensional Hilbert\nspaces has recently been stimulated by the progress in quantum computing,\nquantum-optical state preparation, and measurement techniques, in particular,\nby the development of the discrete quantum-state tomography. In the first part\nof our review we present two essentially different approaches to define\nharmonic oscillator states in the finite-dimensional Hilbert spaces. One of\nthem is related to the truncation scheme of Pegg, Phillips and Barnett [Phys.\nRev. Lett. 81, 1604 (1998)] -- the so-called quantum scissors device. The\nsecond method corresponds to the truncation scheme of Leo\\\u0027nski and Tana\\\u0027s\n[Phys. Rev. A 49, R20 (1994)]. We propose some new definitions of the states\nrelated to these truncation schemes and find their explicit forms in the Fock\nrepresentation. We discuss finite-dimensional generalizations of coherent\nstates, phase coherent states, displaced number states, Schr\\\"odinger cats, and\nsqueezed vacuum. We show some intriguing properties of the states with the help\nof the discrete Wigner function.",
"arxiv_id": "quant-ph/0108080",
"authors": [
"Adam Miranowicz",
"Wieslaw Leonski",
"Nobuyuki Imoto"
],
"categories": [
"quant-ph"
],
"journal_ref": "\"Modern Nonlinear Optics\", ed. M. W. Evans, Advances in Chemical\n Physics, vol. 119 (I) (Wiley, New York, 2001) pp. 155-193",
"title": "Quantum-optical states in finite-dimensional Hilbert space. I. General formalism",
"url": "https://arxiv.org/abs/quant-ph/0108080"
},
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