Photon-added coherent states for exactly solvable Hamiltonians

The evolution of pairwise quantum correlations of Bell cat states under amplitude damping is examined using the concept of quantum discord which goes beyond entanglement. A closed expression of the quantum discord is explicitly derived. We used the Koashi?Winter relation, a relation which facilitates the optimization process of the conditional entropy. We also discuss the temporal evolution of bipartite quantum correlations under a dephasing channel and compare the behaviors of quantum discord and entanglement whose properties are characterized through the concurrence.

https://iopscience.iop.org/article/10.1088/1751-8113/45/32/325302/pdf

Quantum discord of Bell cat states under amplitude damping

We present in this letter a realistic construction of the coherent states for the Morse potential using the Klauder–Perelomov approach. We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated.

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Statistical properties of klauder perelomov coherent states for the morse potential

We continue studying generalized coherent states of the Barut-Girardello type for oscillator-like systems related to a given set of orthogonal polynomials. In this paper we construct a family of coherent states associated with discrete q-Hermite polynomials of the II-type and prove the overcompleteness of this family by constructing the measure in the unity decomposition for this family of coherent states. Bibliography: 49 titles.

Generalized Coherent States for the q-Oscillator Associated with Discrete q-Hermite Polynomials

For the oscillator-like systems, connected with q-Hermite polynomials, coherent states of Barut-Girardello type are defined. The well-known Arik-Coon oscillator naturally arose in the framework of suggested approach as oscillator, connected with the Rogers q-Hermite polynomials, in the same way as usual oscillator with standard Hermite polynomials. The results about the coherent states for discrete q-Hermite polynomials of II type are quite new.

Generalized coherent states for q-oscillator connected with q-Hermite polynomials

The star product and Moyal bracket are introduced using the coherent states corresponding to quantum systems with non-linear spectra. Two kinds of coherent state are considered. The first kind is the set of Gazeau-Klauder coherent states and the second kind are constructed following the Perelomov-Klauder approach. The particular case of the harmonic oscillator is also discussed.

The Moyal bracket in the coherent states framework

The Moyal Bracket in the Coherent States framework

We introduce a special class of truncated Weyl–Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy.

https://iopscience.iop.org/article/10.1088/1751-8113/44/32/325301/pdf

Bipartite and Tripartite Entanglement of Truncated Harmonic Oscillator Coherent States via Beam Splitters

We introduce a special class of truncated Weyl-Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy.

We give a supersymmetric generalization of the sine algebra and the quantum algebra Ut(sl(2)). Making use of the q-pseudo-differential operators graded with a fermionic algebra, we obtain a supersymmetric extension of sine algebra. With this scheme we also get a quantum superalgebra Ut(sl(2/1)).

E. H. El Kinani

Papers

The Moyal bracket in the coherent states framework

The Moyal Bracket in the Coherent States framework

Bipartite and Tripartite Entanglement of Truncated Harmonic Oscillator Coherent States via Beam Splitters

Bipartite and Tripartite Entanglement of Truncated Harmonic Oscillator Coherent States via Beam Splitters

GRADED q-PSEUDO-DIFFERENTIAL OPERATORS AND SUPERSYMMETRIC ALGEBRAS