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Chinese Physics B

Entanglement teleportation via a couple of quantum channels in Ising–Heisenberg spin chain model of a heterotrimetallic Fe–Mn–Cu coordination polymer*

Yidan Zheng, Zhu Mao, Bin Zhou

Published Nov 4, 2019• 17 citations
Publisher

Abstract

We investigate the teleportation of an entangled state via a couple of quantum channels, which are composed of a spin-1/2 Heisenberg dimer in two infinite Ising–Heisenberg chains. The heterotrimetallic coordination polymer CuIIMnII(L1)][FeIII(bpb)(CN)2]·ClO4 · H2O (abbreviated as Fe–Mn–Cu) can be regarded as an actual material for this chain. We apply the transfer-matrix approach to obtain the density operator for the Heisenberg dimer and use the standard teleportation protocol to derive the analytical expression of the density matrix of the output state and the average fidelity of the entanglement teleportation. We study the effects of the temperature T, anisotropy coupling parameter Δ, Heisenberg coupling parameter J 2 and external magnetic field h on the quantum channels. The results show that anisotropy coupling Δ and Heisenberg coupling J 2 can favor the generation of the output concurrence and expand the scope of the successful average fidelity.

DOI
10.1088/1674-1056/ab53cc

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We investigate the teleportation of an entangled state via a couple of quantum channels, which are composed of a spin-1/2 Heisenberg dimer in two infinite Ising–Heisenberg chains. The heterotrimetallic coordination polymer CuIIMnII(L1)][FeIII(bpb)(CN)2]·ClO4 · H2O (abbreviated as Fe–Mn–Cu) can be regarded as an actual material for this chain. We apply the transfer-matrix approach to obtain the density operator for the Heisenberg dimer and use the standard teleportation protocol to derive the analytical expression of the density matrix of the output state and the average fidelity of the entanglement teleportation. We study the effects of the temperature T, anisotropy coupling parameter Δ, Heisenberg coupling parameter J 2 and external magnetic field h on the quantum channels. The results show that anisotropy coupling Δ and Heisenberg coupling J 2 can favor the generation of the output concurrence and expand the scope of the successful average fidelity.
Abstract We demonstrate that two independent spin-1/2 Ising-Heisenberg trimer chains provide an effective platform for the quantum teleportation of any entangled two-qubit state through the quantum communication channel formed by two Heisenberg dimers. The reliability of this quantum channel is assessed by comparing the concurrences, which quantify a strength of the bipartite entanglement of the initial input state and the readout output state. Additionally, we rigorously calculate quantities fidelity and average fidelity to evaluate the quality of the teleportation protocol depending on temperature and magnetic field. It is evidenced that the efficiency of quantum teleportation of arbitrary entangled two-qubit state through this quantum communication channel can be significantly enhanced by moderate magnetic fields. This enhancement can be attributed to the magnetic-field-driven transition from a quantum antiferromagnetic phase to a quantum ferrimagnetic phase, which supports realization of a fully entangled quantum channel suitable for efficient quantum teleportation. The polymeric trimer chains Cu 3 (P 2 O 6 OH) 2 are proposed as an experimental resource of this quantum communication channel, which provides an efficient platform for realization of the quantum teleportation up to moderate temperatures 40 K and extremely high magnetic fields 80 T.
The mixed-spin Ising-Heisenberg and Heisenberg branched chains whose magnetic backbone consists of regularly alternating spins 1/2 and 5/2, the latter of which are additionally coupled to an extra spin 1/2 providing lateral branching, are investigated using exact analytical and density matrix renormalization group (DMRG) methods. The proposed spin-chain models capture some relevant aspects of the heterotrimetallic coordination polymer $[\mathrm{Cu}\mathrm{Mn}(\mathrm{L})][\mathrm{Fe}(\mathrm{bpb}){(\mathrm{CN})}_{2}]\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{Cl}{\mathrm{O}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$. The mixed spin-(1/2,5/2,1/2)(1/2,5/2,1/2)(1/2,5/2,1/2) Ising-Heisenberg branched chain is exactly solvable under the assumption of an Ising-like exchange coupling along the chain, while the lateral branching is treated as an anisotropic XXZXXZXXZ Heisenberg exchange interaction. We determine the ground-state phase diagram and quantify a bipartite quantum entanglement between dimers at lateral branching. It is shown that the studied mixed-spin Ising-Heisenberg branched chain accurately fits available experimental data for temperature dependence of the magnetic susceptibility. The ground-state phase diagram of the analogous mixed spin-(1/2,5/2,1/2)(1/2,5/2,1/2)(1/2,5/2,1/2) Heisenberg branched chain is obtained within the DMRG method. The ground-state phase diagrams of the Ising-Heisenberg and its full Heisenberg counterpart are contrasted. In particular, the ground-state phase diagram of the mixed-spin Heisenberg branched chain involves a special Gaussian critical point, for which a proper finite-size scaling analysis is provided to accurately estimate its location and the correlation length critical exponent.
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.
We investigate the effect of Calogero-Moser (CM) type interactions on the thermal entanglement and teleportation in an anisotropic two-qubit Heisenberg XYZ system with Dzyaloshinskii-Moriya (Dz) interaction in the presence of the external magnetic field. In this regard, the system is designed and analytically solved. The final state density of the system is obtained, and the impact of the system parameters is investigated. The negativity is used to quantify the entanglement dynamics over the system. The generated entangled channels are examined to exchange the information between the system qubits using the standard teleportation protocol; then, the fidelity of the transmitted information is quantified. The effect of the system parameters (Dzyaloshinskii-Moriya, Spin-orbit coupling, CM type interaction, and magnetic field) in the dynamics of the entanglement and state transfer is investigated. Our results indicate that the strength coupling, Dzyaloshinskii-Moriya (Dz) interaction, and magnetic field have a great effect on the dynamics of the entanglement and, consequently, the quality of the generated channels to exchange the information. In addition, we observe that the entanglement of sudden death exists when the distance between the spins is increased.