New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states

In this paper, we investigate how a kind of non-Gaussian states (l-photon excited thermo vacuum state [Formula: see text]) evolves in a single-mode damping channel. We find that it evolves into a Laguerre-polynomial-weighted real–fictitious squeezed thermo vacuum state, which exhibits strong decoherence and its original nonclassicality fades. In particular, when l = 0, in this damping process the thermo squeezing effect decreases while the fictitious-mode vacuum becomes chaotic. In overcoming the difficulty of calculation, we employ the summation method within ordered product of operators, a new generating function formula about two-variable Hermite polynomials is derived.

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New Operator Identities and Integration Formulas Regarding to Hermite Polynomials Obtained via the Operator Ordering Method

International Journal of Theoretical Physics ◽

10.1007/s10773-008-9819-6 ◽

2008 ◽

Vol 48 (2) ◽

pp. 441-448 ◽

Cited By ~ 10

Author(s):

Hong-yi Fan ◽

Tong-tong Wang

Keyword(s):

Hermite Polynomials ◽

Operator Ordering ◽

Integration Formulas

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Vector Product Approach of Producing Non-Gaussian States

International Journal of Theoretical Physics ◽

10.1007/s10773-021-04945-3 ◽

2021 ◽

Author(s):

A. Dehghani ◽

B. Mojaveri ◽

A. A. Alenabi

Keyword(s):

Vector Product ◽

Gaussian States ◽

Product Approach ◽

Non Gaussian

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Teleportation improvement by noiseless linear amplification

Quantum Information and Computation ◽

10.26421/qic19.11-12-3 ◽

2019 ◽

Vol 19 (11&12) ◽

pp. 935-951

Author(s):

Hamza Adnane ◽

Matteo G.A. Paris

Keyword(s):

Coherent States ◽

Large Range ◽

Low Energy ◽

Entangled State ◽

Continuous Variables ◽

Linear Amplification ◽

Gaussian States ◽

Linear Amplifier ◽

Twin Beam ◽

Non Gaussian

We address de-Gaussification of continuous variables Gaussian states by optimal non-deterministic noiseless linear amplifier (NLA) and analyze in details the properties of the amplified states. In particular, we investigate the entanglement content and the non-Gaussian character for the class of non-Gaussian entangled state obtained by using NL-amplification of two-mode squeezed vacua (twin-beam, TWB). We show that entanglement always increases, whereas improved EPR correlations are observed only when the input TWB has low energy. We then examine a Braunstein-Kimble-like protocol for the teleportation of coherent states, and compare the performances of TWB-based teleprotation with those obtained using NL-amplified resources. We show that teleportation fidelity and security may be improved for a large range of NLA parameters (gain and threshold).

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Vehicle Risk Level Estimation by Using Experimental Trajectories in Bend

Volume 9: Transportation Systems; Safety Engineering, Risk Analysis and Reliability Methods; Applied Stochastic Optimization, Uncertainty and Probability ◽

10.1115/imece2011-62055 ◽

2011 ◽

Author(s):

Abdourahmane Koita ◽

Dimitri Daucher ◽

Michel Fogli

Keyword(s):

Probability Density ◽

Reliability Analysis ◽

Probabilistic Models ◽

Hermite Polynomials ◽

Probabilistic Methods ◽

Risk Level ◽

General Context ◽

Risk Levels ◽

Modelling Uncertainties ◽

Non Gaussian

This paper tackles the general context of road safety, focussing on the light vehicles safety in bends. It consists to use a reliability analysis in order to estimate the failure probability of vehicle trajectories. Firstly, we build probabilistic models able to describe measured trajectories in a given bend. The models are transforms of scalar normalized second order stochastic processes which are stationary, ergodic and non-Gaussian. The process is characterized by its probability density function and its power spectral density estimated starting from the experimental trajectories. The probability density is approximated by a development on the Hermite polynomials basis. The second part is devoted to apply a reliability strategy intended to associate a risk level to each class of trajectories. Based on the joint use of probabilistic methods for modelling uncertainties, reliability analysis for assessing risk levels and statistics for classifying the trajectories, this approach provides a realistic answer to the tackled problem.

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