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Revista Mexicana de Física

Two measures elaborated for entangled states: Quantum entropy and fidelity using Schmidt coefficients of the reduced density matrix of full TRI

Rasim Dermez, Yılmaz Tunçer

Published Aug 16, 2022• 0 citations
Publisher

Abstract

In the present study, we determined quantum entanglement in a full trapped ion (TRI)-coherent system and its dependence on the LambDicke parameter (LDP). We investigated the entanglement in view of two elaborated measurements of the family: entropy and fidelity. We selected three values of the deep LDP to demonstrate the benefits of these two critical measures. The findings obtained in this study showed that the maximum value of fidelity for entangled states is quantified approximately to be 0.35, and the long lifetime is also observed with entropy measurement. The findings suggest that three coupling parameters play a significant role in developing quantum entanglement.

DOI
10.31349/revmexfis.68.050703

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In the present study, we determined quantum entanglement in a full trapped ion (TRI)-coherent system and its dependence on the LambDicke parameter (LDP). We investigated the entanglement in view of two elaborated measurements of the family: entropy and fidelity. We selected three values of the deep LDP to demonstrate the benefits of these two critical measures. The findings obtained in this study showed that the maximum value of fidelity for entangled states is quantified approximately to be 0.35, and the long lifetime is also observed with entropy measurement. The findings suggest that three coupling parameters play a significant role in developing quantum entanglement.
In this study, our goal is to obtain the entanglement dynamics of trapped three-level ion interaction two laser beams in beyond Lamb-Dicke parameters. Three values of LDP, η=0.09, η=0.2 and η=0.3 are given. We used the concurrence and the negativity to measure the amount of quantum entanglement created in the system. The interacting trapped ion led to the formation of phonons as a result of the coupling. In two quantum systems (ion-phonons), analytical formulas describing both these measurements are constructed. These formulas and probability coefficients include first order terms of final state vector. We report that long survival time of entanglement can be provided with two quantum measures. Negativity and concurrence maximum values are obtained N = 0.553 and for LDP = 0.3. As a similar, the other two values of LDP are determined and taken into account throughout this paper. For a more detailed understanding of entanglement measurement results, “contour plot” was preferred in Mathematica 8.
The entangled states of three-level of trapped ion and two phonons (into coherent state) in Lambda configuration forming a Hilbert space of 12-dimensional (D) are analyzed. The concurrence is considered "such as a quantum measure" in trapped ion-coherent state system. Four values of Lamb-Dicke parameter (LDP), eta=0.005, 0.07, 0.08$ and $0.09 are investigated by the worths of concurrence. We demonstrate that as eta is increased, sudden birth of entangled states in the system is increased. Thus, establishing of entangled states can be tuned by LDP.
In the present communication we explore and develop the theory of entanglement measures. As a result we obtain a general criterion of a bipartite mixed states entanglement due to the quasi-mutual entropy for a single trapped two-level ion interacting with a laser field. This general expression of the entanglement degree is obtained with the physical significance and without the diagonal approximation. We indicate how the entanglement affected by different values of the Lamb-Dicke parameter of the initially generalized binomial state. Among the new features found, it is shown, for the large number of quanta, that the shape of entanglement could oscillate around the maximum value, which is related to the existence of a strong entanglement in the present system.
he dynamical properties of quantum entanglement in a time-dependent three-level-trapped ion interacting with a laser field are studied in terms of the reduced-density linear entropy considering two specific initial states of the field. Allowing the instantaneous position of the center-of-mass motion of the ion to be explicitly time-dependent, it is shown that either sudden death of entanglement or survivability of quantum entanglement can be obtained with a specific choice of the initial state parameters. The difference in evolution picture corresponding to the multi-quanta processes is discussed.
A quantum scheme is presented by which a three-level trapped ion interacts with a two laser beams in the absence and presence of the e®ect of classical field. We analyze the impact of the classical ¯eld and the Lamb-Dicke parameter (LDP) on the dynamical behavior of entanglement quanti¯er, population probabilities and the geometric phase. Based on four different variations of these two effects, LDP = 0.1, LDP=0.01 and ¯ = 0.0, ¯ = 0.49, the time dependence of geometric phase and populations probabilities are shown. The ¯nding emphasizes that both the time-dependent and LDP play an important role in the development of the entanglement, the geometric phase, ¯delity, and populations probabilities. This in-sight may be very useful in various applications in quantum optics and information processing.