Fidelity and concurrence of entangled qudits between a trapped ion and two laser beams

Abstract

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.

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

“…3 and 4. These findings are consistent with the findings obtained in previous studies [19,21,25]. We can see in Fig.…”

“…There are both contributions and compatibilities between Ref. [25]'s fidelity calculations and this paper.…”

“…With the help of the basic formulas in Ref. [25], we obtained the fidelity of the system as follow: [28,29]…”