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Acta Physica Slovaca Reviews and Tutorials

Quantum state engineering in finite-dimensional Hilbert space

Adam Miranowicz, W. Leoński, Sigurd Dyrting, R. Tanaś

Published Jun 1, 1996• 17 citations
OpenAlex

Abstract

We give a recipe for how to generate various harmonic oscillator states formally defined in finite-dimensional Hilbert space.

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This chapter presents two essentially different constructions of harmonic oscillator states in a finite-dimensional (FD) Hilbert space. The authors propose some new definitions of the states and find their explicit forms in the Fock representation. For the convenience of the reader, they bring together several known FD quantum-optical states, including FD coherent states, FD phase coherent states, FD displaced number states, FD Schrödinger cats, and FD squeezed vacuums. The discrete Wigner function is applied in order to demonstrate intriguing properties of the various states.
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