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Scientific Reports

Pairwise quantum criteria and teleportation in a spin square complex

Fadwa Benabdallah, Saeed Haddadi, Hamid Arian Zad, Mohammad Reza Pourkarimi, Mohammed Daoud A, N.S. Ananikian

Published Apr 18, 2022• 36 citations
Publisher

Abstract

Thermal non-classical correlations quantified by concurrence entanglement, local quantum uncertainty, and quantum coherence in a four-qubit square chain are exactly examined. The influences of the Hamiltonian parameters on the mentioned pairwise quantum criteria and fidelity of teleportation are studied, and the most interesting findings are discussed in detail. It is found that the tuning anisotropy results in enhancing the thermal quantum correlations and coherence as well as average fidelity until achieving maximum values. We persuasively deduce that quantum coherence is a more efficient criterion than that of concurrence and local quantum uncertainty to detect the quantumness of a thermal state.

DOI
10.1038/s41598-022-10248-2

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•Sep 1, 2021•0 citations
Thermal non-classical correlations quantified by concurrence entanglement, local quantum uncertainty, and quantum coherence in a four-qubit square chain are exactly examined. The influences of the Hamiltonian parameters on the mentioned pairwise quantum criteria and fidelity of teleportation are studied, and the most interesting findings are discussed in detail. It is found that the tuning anisotropy results in enhancing the thermal quantum correlations and coherence as well as average fidelity until achieving maximum values. We persuasively deduce that quantum coherence is a more efficient criterion than that of concurrence and local quantum uncertainty to detect the quantumness of a thermal state.
In this paper, the features of quantum teleportation of a maximally entangled input thermal state using a system, consisting of two qubits (spin-1/2) anisotropic XY Heisenberg model with Herring–Flicker coupling in the presence of a magnetic field, are discussed. So, we study the influence on the thermal entanglement of different physical parameters such as temperature [Formula: see text], magnetic field [Formula: see text], degree of anisotropy [Formula: see text] and distance [Formula: see text] between the two spins. The goal is to determine the conditions of use of the system as a good channel to promote quantum teleportation. The amount of output entanglement is quantified by the concurrence [Formula: see text], and the quality of teleportation is analyzed using the concept of fidelity [Formula: see text]. It is shown that [Formula: see text] presents a maximum at extremely low temperature for a large range of the parameter [Formula: see text]. Also, when we increase the temperature, we observe a dissipation of the appropriate range of [Formula: see text] and the decrease of the amplitude of [Formula: see text]. Besides, under an external magnetic field [Formula: see text], we show the appearance of quantum phase transitions with the entanglement vanishing when the condition [Formula: see text] is fulfilled, then the system can ensure the ideal communication transmission. Concerning the Ising model [Formula: see text] in the ground state, the output entanglement is nonzero only in the presence of the magnetic field [Formula: see text], and this model is useful for ensuring a distorted transmission. At finite temperature, the fidelity [Formula: see text] is less than the value 2/3, so that the system is useless as a quantum channel for providing quantum teleportation.
This paper investigates the thermal pairwise entanglement of a three-qubit Heisenberg XXZ chain in the presence of the Dzyaloshinski–Moriya (DM) anisotropic antisymmetric interaction and quantum teleportation when using the Heisenberg chain as a channel. The entanglement dependences on the DM interaction and temperature are given in detail. It obtains the relation between the concurrence and average fidelity, and shows that the same concurrence can lead different average fidelities. Moreover, it finds the thermally entangled states which do not violate the Bell inequalities, and can still be used for quantum teleportation.
Abstract The thermal quantum correlations in a two-qubit one-dimensional XXZ Heisenberg spin- 1 2 chain subjected to an inhomogeneous magnetic field are investigated. The concurrence, as thermal entanglement quantifier, and the discord-like quantifiers, namely the trace distance discord and local quantum uncertainty, are computed. Their dependence on the anisotropy parameter γ , uniform magnetic field B , coupling constant J and nonuniform magnetic field b are presented in detail. The mentioned quantifiers behaviors in terms of this parameters are compared and discussed. The results show that TDD is always much stronger than the concurrence and LQU, whereas the latter two show a swinging behavior depending on system parameters. Also, we have shown that the nonuniform magnetic field can reduce the effects of temperature on thermal correlations. Furthermore, the thermal correlations, for fixed values of b , can be enhanced in the antiferromagnetic system in comparison to the ferromagnetic one. In addition, the quantum correlations amounts in the ferromagnetic system are deteriorated when γ decreases, but they are improved when the system is antiferromagnetic.
The quantum teleportation with the entangled thermal state is investigated based on the completely anisotropic Heisenberg chain in the presence of the externally inhomogeneous magnetic field. The effects of the anisotropy and magnetic field for the quantum fidelity are studied in detail. The zero temperature limit and the features of the nonzero temperature for this nonclassical fidelity are obtained. We find that the quantum teleportation demands more stringent conditions than the thermal entanglement of the resource by investigating the threshold temperature of the thermal concurrence and the critical temperature of the maximal teleportation fidelity. The useful quantum teleportation should avoid the point of the phase transition of the system and the anisotropy of the chain and the external magnetic field can control the applicability of the resource in the quantum teleportation.
In this paper, thermal entanglement in four and five-qubit spin-star networks evolved by an XXX Hamiltonian model is studied. We examine the effect of temperature, magnetic field and coupling constant on the concurrence. We will show that the entanglement is decreased by increasing the temperature and the number of qubits. Also, we investigate quantum teleportation via a couple of spin-star networks in a thermal state. The average of fidelity as a function of temperature, magnetic field, and coupling constant is analyzed, too. It will be observed that as the temperature increases, the fidelity first decreases and then tends to a constant value. Moreover, with the increase of the external magnetic field, the average fidelity first increases and then gradually decreases, and in a certain amount of magnetic field, the average fidelity becomes zero. In addition, as the number of qubits increases, fidelity decreases with temperature. The results indicate that mean fidelity increases with increasing coupling constant.