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## On-line version ISSN 2007-9737Print version ISSN 1405-5546

#### Abstract

AVILA AOKI, Manuel; HONORATO, Carlos Gerardo  and  HERNANDEZ VAZQUEZ, Jose Eladio. Time Evolution of the 3-Tangle of a System of 3-Qubit Interacting through a XY Hamiltonian. Comp. y Sist. [online]. 2019, vol.23, n.2, pp.469-476.  Epub Mar 10, 2021. ISSN 2007-9737.  https://doi.org/10.13053/cys-23-2-2309.

We consider a pure 3-qubits system interacting through a XY-Hamiltonian with antiferromagnetic constant J. We employ the 3-tangle as an efficient measure of the entanglement between such a 3-qubit system. The time evolution of such a 3-tangle is studied. In order to do the above, the 3-tangle associated to the pure 3-qubit state $|\psi \left(t\right)⟩={c}_{0}\left(t\right)|000⟩+{c}_{1}\left(t\right)|001⟩+{c}_{2}\left(t\right)|010⟩+{c}_{3}\left(t\right)|011⟩+{c}_{4}\left(t\right)|100⟩+{c}_{5}\left(t\right)|101⟩+{c}_{6}\left(t\right)|110⟩+{c}_{7}\left(t\right)|111⟩$ is calculated as a function of the initial coefficients $\left\{{c}_{i}\left(t=0\right)\right\}\left(i=0,1,\dots ,7\right)$, the time t and the antiferromagnetic constant J. We find that the 3-tangle of the 3-qubit system is periodic with period $t=4\pi /J$. Furthermore, we also find that the 3-tangle as a function of the time t and J has maximal and minimum values. The maximal values of the 3-tangle can be employed in Quantum Information Protocols (QIP) that use entanglement as a basic resource. The pattern found for the 3-tangle of the system of three qubits interacting through a XY Hamiltonian as a function of J and the time t resembles to a quantized physical quantity.

Keywords : 3-qubits; non-classical communications; quantum information processing; entanglement.

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