Abstract A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not order embeddable into the standard quantum logic, the lattice L(𝓗) of all closed subspaces of a separable complex Hilbert space. We show that a finite generalized effect algebra is order embeddable into the standard effect algebra E(𝓗) of effects of a separable complex Hilbert space iff it has an order determining set of generalized states iff it is order embeddable into the power of a finite MV-chain. As an application we obtain an algorithm, which is based on the simplex algorithm, deciding whether such an order embedding exists and, if the answer is positive, constructing it.Abstract A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not order embeddable into the standard quantum logic, the lattice L(𝓗) of all closed subspaces of a separable complex Hilbert space. We show that a finite generalized effect algebra is order embeddable into the standard effect algebra E(𝓗) of effects of a separable complex Hilbert space iff it has an order determining set of generalized states iff it is order embeddable into the power of a finite MV-chain. As an application we obtain an algorithm, which is based on the simplex algorithm, deciding whether such an order embedding exists and, if the answer is positive, constructing it.

Mathematica SlovacaApr 1, 20161 citation

Some Problems for Sequential Effect Algebras

Longsuo Li, Lai-zhen Luo, Junde Wu

International Journal of Theoretical PhysicsDec 23, 20100 citations

COHERENT STATES FOR NONLINEAR TWO-BOSON REALIZATION OF THE ISOTROPIC OSCILLATOR ALGEBRA ON A SPHERE

Ali Mahdifar

In this paper, we generalize Schwinger realization of the 𝔰𝔲(2) algebra to construct a two-mode realization for deformed 𝔰𝔲(2) algebra on a sphere. We obtain a nonlinear (f-deformed) Schwinger realization with a deformation function corresponding to the curvature of sphere that in the flat limit tends to unity. With the use of this nonlinear two-mode algebra, we construct the associated two-mode coherent states (CSs) on the sphere and investigate their quantum entanglement. We also compare the quantum statistical properties of the two modes of the constructed CSs, including anticorrelation and antibunching effects. Particularly, the influence of the curvature of the physical space on the nonclassical properties of two modes is clarified.In this paper, we generalize Schwinger realization of the 𝔰𝔲(2) algebra to construct a two-mode realization for deformed 𝔰𝔲(2) algebra on a sphere. We obtain a nonlinear (f-deformed) Schwinger realization with a deformation function corresponding to the curvature of sphere that in the flat limit tends to unity. With the use of this nonlinear two-mode algebra, we construct the associated two-mode coherent states (CSs) on the sphere and investigate their quantum entanglement. We also compare the quantum statistical properties of the two modes of the constructed CSs, including anticorrelation and antibunching effects. Particularly, the influence of the curvature of the physical space on the nonclassical properties of two modes is clarified.

International Journal of Geometric Methods in Modern PhysicsJun 3, 20135 citations

Algebraic Formulation of the Operatorial Perturbation Theory. Part 2. Aplications

Ary W. Espinosa Müller, Adelio Matamala-V�squez

The algebraic approach to operator perturbation method has been applied to two quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator'' and ``The Generalized Zeeman Effect''. To that end, two realizations of the superoperators involved in the formalism have been carried out. The first of them has been based on the Heisenberg--Dirac algebra of $\hat{a}^\dagger$ , $\hat{a}$ , $\hat{1}$ operators, the second one has been based in the angular momemtum algebra of $\hat{L}_+$ , $\hat{L}_-$ and $\hat{L}_0$ operators. The successful results achieved in predicting the discrete spectra of both systems have put in evidence the reliability and accuracy of the theory.The algebraic approach to operator perturbation method has been applied to two quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator'' and ``The Generalized Zeeman Effect''. To that end, two realizations of the superoperators involved in the formalism have been carried out. The first of them has been based on the Heisenberg--Dirac algebra of $\hat{a}^\dagger$, $\hat{a}$, $\hat{1}$ operators, the second one has been based in the angular momemtum algebra of $\hat{L}_+$, $\hat{L}_-$ and $\hat{L}_0$ operators. The successful results achieved in predicting the discrete spectra of both systems have put in evidence the reliability and accuracy of the theory.

arXiv:quant-ph/9606013Jun 13, 19960 citations

Sequential products on effect algebras

Stanley Gudder, Richard J. Greechie

Reports on Mathematical PhysicsFeb 1, 2002127 citations

\hat{a}^\dagger

\hat{a}

\hat{1}

operators, the second one has been based in the angular momemtum algebra of

\hat{L}_+

\hat{L}_-

and

\hat{L}_0

operators. The successful results achieved in predicting the discrete spectra of both systems have put in evidence the reliability and accuracy of the theory.