Coherent states in a finite-dimensional basis: Their phase properties and relationship to coherent states of light

Generalized measurements via a programmable quantum processor

“…Here we follow the notation introduced in Ref. [16]. Let the N -dimensional Hilbert space be spanned by N orthogonal normalized vectors |x k or, equivalently, by N vectors |p l , k, l = 0, .…”

Quantum-Optical States in Finite-Dimensional Hilbert Space. I. General Formalism

“…In the 1990s, various quantum-optical states were constructed in FD Hilbert spaces in analogy to those in the ID spaces. In particular, (1) various kinds of FD coherent states [16]- [24], (2) FD displaced number states [21], (3) FD even and odd coherent states [25,21,24], (4) FD phase states [26], (5) FD phase coherent states (also referred to as coherent phase states) [27]- [30], (6) FD squeezed states [31]- [34], (7) FD displaced phase states [28], or (8) FD even and odd phase coherent states [35]. The interest in the FD quantum-optical states has been stimulated by the progress in quantum-optical state preparation and measurement techniques [36], in particular, by the development of the discrete quantum-state tomography [37]- [42].…”

Quantum-Optical States in Finite-Dimensional Hilbert Space. II. State Generation

“…We shall concentrate on the states proposed by Bužek et al [2] and further discussed by Miranowicz et al [3,23], where both the Glauber displacement operator and the states are defined in the FD Hilbert space [1]. The method of generation discussed here is based on the quantum systems containing a Kerr medium represented by nonlinear oscillator.…”

“…For instance, various kinds of FD coherent states [2]- [6], FD Schrödinger cats [5,6,7], FD displaced number states [5], FD phase states [8], FD squeezed states [9,10] were studied by many authors. In this chapter we concentrate on some schemes of generation of the FD quantum-optical states.…”

“…Namely, we shall describe the models involving quantum nonlinear oscillator driven by an external field [11,12,13,22]. For this class of systems we are able to get the quantum states that are very close for instance, to the FD coherent states [2,3] or to the FD squeezed vacuum [10].…”