Time Evolution of the 3-Tangle of a System of 3-Qubit Interacting through a XY Hamiltonian

Resumen

We consider a pure 3-qubits system interacting through a XY-Hamiltonian with antiferromagneticconstant 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 j (t)i = c0(t)j000i + c1(t)j001i + c2(t)j010i + c3(t)j011i + c4(t)j100i + c5(t)j101i + c6(t)j110i + c7(t)j111i is calculated as a function of the initial coefficients fci (t = 0)g (i = 0, 1, ..., 7), the timet and the antiferromagnetic constant J. We find that the 3-tangle of the 3-qubit system is periodic with periodt = 4=J. Further more, we also find that the 3-tangle asa 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.