The Geometry Of Four Quantum Entanglement Measurement

Entanglement is the center issue in quantum information. Entangled states havediferent remarkable applications, and among them are quantum cryptography, quantumsuperdense coding and quantum computing etc.. The reason for using the geometricmeasure of entanglement is that it is suitable for any partite system regardless of itsdimensions. However, analytical computation for generic states still remains as a greatchallenge. The measure depends on entanglement eigenvalue Λ~2maxand can be derived from the formula max. For pure states, the entanglement eigenvalue is equalto the maximal overlap of a given state with any complete product state. The basic ideais to use (n-1) qubit mixed states to calculate the geometric measure of n qubit purestates. On the basis of geometric measure of entanglement of three-qubit pure states, wegive the theory of geometric measure of four-qubit pure states system. And the concretecalculate method has been given. Through the example of GHZ states, W states and otherforms of states, we enrich the theory of geometric measure of entanglement of four-qubitpure states.