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International Conference on Micro- and Nano-Electronics (ICMNE)

Quantum entanglement in spin chains with the XY Hamiltonian at the quantum state transfer

E. I. Kuznetsova, I. D. Lazarev

Published Mar 15, 2019• 0 citations
Publisher

Abstract

In the present work the generation of entanglement between the receiver and sender is investigated in the process of the quantum state transfer in the homogeneous one-dimensional chain of spins 1/2 with the XY -Hamiltonian in the approximation of the nearest neighbour interactions. Fidelity is obtained for a quantum state transfer for various numbers of spins and temperatures and values of initial polarisation of the sender’s spin. The transmitted pure state is encoded in the state of first spin (sender) in the initial time moment. The other spins are in the thermodynamic equilibrium state. The reduced density matrix for the receiver and the sender is obtained for an investigation of entanglement in the “sender-receiver” system. The effect of temperature and polarization of the transmitted state on the generation of entanglement in the system is also investigated.

DOI
10.1117/12.2521624

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In the present work the generation of entanglement between the receiver and sender is investigated in the process of the quantum state transfer in the homogeneous one-dimensional chain of spins 1/2 with the XY -Hamiltonian in the approximation of the nearest neighbour interactions. Fidelity is obtained for a quantum state transfer for various numbers of spins and temperatures and values of initial polarisation of the sender’s spin. The transmitted pure state is encoded in the state of first spin (sender) in the initial time moment. The other spins are in the thermodynamic equilibrium state. The reduced density matrix for the receiver and the sender is obtained for an investigation of entanglement in the “sender-receiver” system. The effect of temperature and polarization of the transmitted state on the generation of entanglement in the system is also investigated.
We investigate entanglement of spin pairs in alternating open spin chains ( s = 1/2) with spin-spin interactions (SSI) in the thermodynamic equilibrium state in an external magnetic field. The reduced density matrix of an arbitrarily chosen spin pair was calculated. The entanglement of a spin pair was evaluated with the Wootters criterion. The temperature at which the entangled state arises in the chosen pair was determined. Entanglement (concurrence) is shown to oscillate as a function of the position of a spin pair in the chain. The results demonstrate the dependence of the entanglement in arbitrarily chosen pairs of neighboring spins on the temperature, the position of the spin pair in the chain, chain length, and the ratio between the SSI constants. Qualitative explanation of these dependences is offered. The role of the terminal spins in the generation of entanglement is explained.
We propose a protocol restoring the state transferred along the spin chain governed by the XY-Hamiltonian. Such dynamics does not preserve the excitation number and leads to mixing multiple-quantum coherence matrices of orders having the same parities. Depending on the initial state, this results in generating either all possible or only even-order multiple-quantum coherence matrices. Restoring is established via the special unitary transformation applied to the receiver side of the chain (extended receiver). An example of restoring [Formula: see text]- and [Formula: see text]-order coherence matrices in two-qubit state transfer is considered. Entanglement transfer in such process is also studied and possibility of its amplification is demonstrated.
The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A72 (2005) 012331]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For generating W-state and GHZ-state a single qubit rotation is applied on second and all the three qubits, respectively after the unitary evolution of the XY Hamiltonian.
We consider an unmodulated linear spin chain composed of two qubits at the ends, which undergo nearest-neighbor interactions, with an arbitrary spin between them. The state of the qubit on one end is to be transmitted through the arbitrary spin and is received by the qubit on the other end with some fidelity. We look at the behavior of the average f idelity of state transfer through time as affected by the spin quantum number of the arbitrary spin in between the qubits. We f ind that the higher the spin quantum number becomes, the earlier it takes to achieve perfect or nearly perfect state transfer. Moreover, when the channel with arbitrary spin is subjected to environment interaction, results from the calculation of average fidelity suggest that increasing the spin quantum number of the channel provides a countermeasure to the effects of decoherence induced by the environment.
We initially introduce one-dimensional mixed-five-spin chain with Ising- XY model which includes mixture of spins-1/2 and spins-1. Here, it is considered that nearest spins (1,1/2) have Ising-type interaction and nearest spins (1/2,1/2) have both XY -type and Dzyaloshinskii–Moriya (DM) interactions together. Nearest spins (1,1) have XX Heisenberg interaction. This system is in the vicinity of an external homogeneous magnetic field B in thermal equilibrium state. We promote the quantum information transmitting protocol verified for a normal spin chain with simple model (refer to Rossini D, Giovannetti V and Fazio R 2007 Int. J. Quantum Infor. 5 439) (widely in reference: Giovannetti V and Fazio R 2005 Phys. Rev. A 71 032314) by means of considering the suggested mixed-five-spin chain as a quantum communication channel for transmitting both qubits and qutrits ideally. Hence, we investigate some useful quantities such as quantum capacity and quantum information transmission rate for the system. Finally, we conclude that, when the DM interaction between spins (1/2,1/2) increases the system is a more ideal channel for transmitting information.