The Relations of Reduced Density Matrices and the N-Tangle for Even-N Qubit States

N-tangle is a measure of entanglement in a mixed state through reduced density matrices. In this paper, we present a relationship between reduced density matrices and the n-tangle for even-N qubit states. For n- qubit states, the n-tangle can be determined by reduced density matrices of rho(1), rho(12), MIDLINE HORIZONTAL ELLIPSIS rho(12MIDLINE HORIZONTAL ELLIPSISn/2), etc. Further, we also determined relations for even-qubit states from two to ten qubits of pure state. Finally, we generalize the relationship between the reduced density matrices and the n-tangle for even-N qubit states. The results have the potential for experimental quantification of entanglement along with possible interpretation.

Automated summary

In this paper, the relationship between reduced density matrices and the n-tangle for even-N qubit states is presented. The paper also determines relations for even-qubit states from two to ten qubits of pure state. Furthermore, the generalization of the relationship between the reduced density matrices and the n-tangle for even-N qubit states is discussed.