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Laser Physics Letters

Two forms for 3-uniform states of eight-qubits

Xin-Wei Zha, Da Zhang, Irfan Ahmed, Yanpeng Zhang

Published Apr 12, 2018• 7 citations
Publisher

Abstract

Abstract In this paper, we study the relations between average bipartite entanglement and the n -tangle of eight-qubits. We have derived two forms for 3-uniform states of eight-qubits. One form has the n -tangle equal to zero; the other form has the n -tangle equal to unity.
DOI
10.1088/1612-202x/aab69d

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Gilad Gour and Nolan R Wallach [J. Math. Phys. 51 112201 (2010)] have proposed the 4-tangle and the square of the I concurrence. They also gave the relationship between the 4-tangle and the square of the I concurrence. In this paper, we give the expression of the square of the I concurrence and the n-tangle for six-qubit and eight-qubit by some local unitary transformation invariant. We prove that in six-qubit and eight-qubit states there exist strict monogamy laws for quantum correlations. We elucidate the relations between the square of the I concurrence and the n-tangle for six-qubit and eight-qubits. Especially, using this conclusion, we can show that 4-uniform states do not exist for eight-qubit states.
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The bipartite and tripartite entanglement in a three-qubit Heisenberg XY model with a nonuniform magnetic field is studied. There are two or four peaks in the concurrence of the bipartite entanglement when the amplitudes of the magnetic fields are differently distributed between the three qubits. It is very interesting to note that there is no tangle of tripartite entanglement between the three qubits when the amplitudes of the magnetic fields are varied. However, the variation of the magnetic field direction can induce the tangle. The tangle is periodic about the angle between the magnetic field and the z axis of the spin.