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Abstract

Entanglement is an interesting feature of quantum theory, which in recent years has attracted many researchers to quantify, classify and to investigate its useful properties. Entanglement has already some applications such as quantum teleportation and quantum key distribution, and there will be new applications for this fascinating quantum phenomenon. For example, multipartite entanglement has the capacity to offer new unimaginable applications in emerging fields of quantum information and quantum computation. I will propose concurrence classes for general pure multipartite states based on an orthogonal complement of a positive operator valued measure on quantum phase. In particular, I will construct $W^{m}$ class, $GHZ^{m}$, and $GHZ^{m-1}$ class concurrences for general pure $m$-partite states. I will give analytical expressions for $W^{3}$ and $GHZ^{3}$ class concurrences for general pure three-partite states and for $W^{4}$, $GHZ^{4}$, and $GHZ^{3}$ class concurrences for general pure four-partite states.