1211.6472 (Andrzej M. Frydryszak et al.)

Geometric measure of entanglement of the qubit with an arbitrary quantum
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Andrzej M. Frydryszak, Volodymyr M. Tkachuk

We find the explicit expression for geometric measure of entanglement of one qubit with arbitrary other quantum system. The result is applied to the characterization of the bipartite entanglement of the Werner state, Dicke state, GHZ state and trigonometric states for systems consisting of $n$ qubits. The geometric measure of entanglement of one qubit with other $n-1$ qubits in above states is calculated and general properties of bipartite entanglement are established. In particular for the Werner-like states the rule of sums is found and it is shown that deviations from the symmetricity of such states diminishes the amount of entanglement. For Dicke states we show that the maximal value of bipartite entanglement is achieved when number of excitations is half of the total number of qubits in these state. For trigonometric states the bipartite entanglement is maximal and does not depend on the number of qubits.

View original: http://arxiv.org/abs/1211.6472