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Physica Scripta

Study different quantum teleportation amounts by solving Lindblad master equation

K. El Anouz, Abderrahim El Allati, Farhan Saif

Published Jan 31, 2022• 6 citations
Publisher

Abstract

Abstract A realizable model based on the interaction between an excited two-level atom and a radiation field inside two quantum electrodynamics cavities is proposed. It consists of sending the excited atom through two serial cavities which contain the radiation field. Thus, the Lindblad master equations which describe the evolution of the reduced density matrix regarding the radiation field generated from the excited atom inside the cavities are solved in Markovian and non-Markovian regimes. Thereby, the rate of entanglement inherent in the total field-field system is evaluated using various witnesses by calculating analytically the concurrence and quantum discord, where we illustrate quantitatively the advantage of using an initial EPR and NOON states in the presence of radiation field losses. As an application, a scheme of quantum teleportation using two partial entangled channels is investigated. Finally, a comparative study between fidelity and the different levels of entanglement of the teleported state in the two regimes is also given.

DOI
10.1088/1402-4896/ac5084

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Abstract A realizable model based on the interaction between an excited two-level atom and a radiation field inside two quantum electrodynamics cavities is proposed. It consists of sending the excited atom through two serial cavities which contain the radiation field. Thus, the Lindblad master equations which describe the evolution of the reduced density matrix regarding the radiation field generated from the excited atom inside the cavities are solved in Markovian and non-Markovian regimes. Thereby, the rate of entanglement inherent in the total field-field system is evaluated using various witnesses by calculating analytically the concurrence and quantum discord, where we illustrate quantitatively the advantage of using an initial EPR and NOON states in the presence of radiation field losses. As an application, a scheme of quantum teleportation using two partial entangled channels is investigated. Finally, a comparative study between fidelity and the different levels of entanglement of the teleported state in the two regimes is also given.
An experimentally realizable model based on the interaction between an excited two-level atom and a radiation field inside two quantum electrodynamics cavities is proposed. It consists of sending an excited two-level atom through two serial cavities which contain the radiation field. Hence, the Lindblad master equation described the reduced density matrix of the joint-joint field system inside the cavities is exactly solved in Markovian and non-Markovian regimes. However, the rate of entanglement inherent in the total field-field system are evaluated using various witnesses of entanglement such as concurrence, logarithmic negativity and quantum discord. Moreover, the non-classicality by means of negativity volume and Wigner function is discussed. Finally, two schemes of quantum teleportation are suggested.
A scheme of quantum teleportation using Jaynes–Cummings model is proposed. It consists of using a partial entangled state generated from the interaction between a two-level atom and single mode of radiation field as a quantum channel. By controlling the number of photons inside cavity and detuning parameter, the dynamical evolution of quantum correlation and entanglement degree in terms of quantum discord and concurrence, respectively, in the nonresonance case are investigated. Moreover, a comparative study between the teleported entanglement, teleported quantum correlation and average fidelity shows a good similarity between their dynamical evolution. Consequently, we conclude that quantum discord may be considered as a good information source in quantum teleportation process.
We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance r and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption, but no Born or Markov approximation. We derived a non-Markovian master equation for the evolution of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. It contains a Markovian part with a Lindblad type operator and a nonMarkovian contribution, the physics of which is the main focus of this study. We use the concurrence function as a measure of quantum entanglement between the two qubits. Two classes of states are studied in detail: Class A is a one parameter family of states which are the superposition of the highest energy |I〉 ≡ |11〉 and lowest energy |O〉 ≡ |00〉 states, υiz, |A〉≡p|I〉+(1−p)|O〉, with 0 ≤ p ≤ 1; and Class B states |B〉 are linear combinations of the symmetric |+〉=12(|01〉+|10〉) and the antisymmetric |−〉=12(|01〉−|10〉) Bell states.
We propose a scheme for the teleportation of an unknown two-particle entangled EPR state without the Bell-state measurement.Alice needs to teleport an unknown two-particle EPR state to Bob.Her atoms and Bob's are prepared in the maximal entangled GHZ state,which forms the quantum channel.She sends two atoms through a single-mode cavity field,and drives them by a strong classical field at the same time.Throngh the interaction between the atoms and the cavity,the states of these atoms are evolved.After the interaction,Alice realizes the teleportation successfully.In the scheme,the effects of thermal field and cavity decay are all eliminated.The success probability is 1.0,and the fidelity is 1.0 too.
In this paper, we propose a protocol for teleportation of two unknown atomic states using non-maximally entangled states. We consider teleportation for atomic entangled states in cavity quantum electrodynamics (QED). Through analysis, we conclude that it could be succeed without joint BSM (Bell-State measurement). One BSM can be exactly converted into two separate atomic measurements on the two relevant atoms only by one step using the interaction between the atoms and atoms in the cavity. The most remarkable advantage of our scheme is that the teleportation and distillation procedure can be carried out concurrently. Suppose that the cavity mode is prepared in vacuum state. We can utilize the Hamiltonian for the system, discussing how to make teleportation successful. And we discuss the probability of reconstructing the initial state. We consider two identical two-level atoms simultaneously interacting with a single-mode cavity field. There is no energy exchange between the atomic system and the cavity, so we use the detuned interaction between atoms and atoms in cavity in the scheme which is insensitive to both the cavity decay and the thermal field. For the resonant cavity, in order to realize the teleportation successfully, the relationship between the teleportation time and the excited atom lifetime should take into consideration. The time required to complete the teleportation should much shorter than that of atom radiation. Hence, atom with a sufficiently long excited lifetime should be chosen. The discussion of the scheme indicates that it can be realized by current technologies.
The aim of this paper is investigation on dynamics of super quantum discord (SQD) and quantum discord (QD) teleportation in the Jaynes–Cummings model. In order to teleport one and two qubit states, a scheme is proposed for quantum channel where is induced from an atom-field interaction. The initial state of the atom is its excited state while the state of field starts in a coherent one. The model reveals that the dynamics of quantum correlations depends crucially on atom-field initial conditions and the field parameters can be utilized as control parameters for optimal teleportation. Interestingly, we find that QD teleportation and SQD teleportation are not always zero when the entanglement falls to zero for a teleported state. This result clearly illustrates that in some cases we can only get a truly quantum teleportation by QD and SQD if we use a suitable field parameters and initial state, which have no entanglement. The results reveal that QD and SQD for teleported states are much robuster than entanglement in the process of communication. According to the results, the proposed scheme can greatly reduce the cost of quantum communication. We also obtain that the behaviour of the QD and SQD teleportation are similar to average fidelity. So, QD and SQD can be used to analyse teleported state as average fidelity.