A class of quantum gate entangler

We construct quantum gate entanglers for different classes of multipartite states based on definition of W and GHZ concurrence classes. First, we review the basic construction of concurrence classes based on orthogonal complement of a positive operator valued measure (POVM) on quantum phase. Then, we construct quantum gates entanglers for different classes of multi-qubit states. In particular, we show that these operators can entangle multipartite state if they satisfy some conditions for W and GHZ classes of states. Finally, we explicitly give the W class and GHZ classes of quantum gate entanglers for four-qubit states.Comment: 5 pages, accepted for publication in Physica Scripta for the CEWQO2009 proceedings

Concurrence for multipartite states

We construct a generalized concurrence for general multipartite states based on local W-class and GHZ-class operators. We explicitly construct the corresponding concurrence for three-partite states. The construction of the concurrence is interesting since it is based on local operators.Comment: 5 page

Noncommutative geometrical structures of entangled quantum states

We study the noncommutative geometrical structures of quantum entangled states. We show that the space of a pure entangled state is a noncommutative space. In particular we show that by rewritten the conifold or the Segre variety we can get a $q$-deformed relation in noncommutative geometry. We generalized our construction into a multi-qubit state. We also in detail discuss the noncommutative geometrical structure of a three-qubit state.Comment: 7 page

Geometrical structures of multipartite quantum systems

In this paper I will investigate geometrical structures of multipartite quantum systems based on complex projective varieties. These varieties are important in characterization of quantum entangled states. In particular I will establish relation between multi-projective Segre varieties and multip-qubit quantum states. I also will discuss other geometrical approaches such as toric varieties to visualize complex multipartite quantum systems.Comment: 5 pages, Talk given at The Seventh International Conference Quantum Theory and Symmetries (QTS-7), Prague, August 7-13, 201

Geometry and structure of quantum phase space

The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an important role in foundations of quantum mechanics and quantum information. In this work we discuss a geometric framework for mixed quantum states represented by density matrices, where the quantum phase space of density matrices is equipped with a symplectic structure, an almost complex structure, and a compatible Riemannian metric. This compatible triple allow us to investigate arbitrary quantum systems. We will also discuss some applications of the geometric framework.Comment: 7 pages, talk given at the conference on Quantum Theory: from Problems to Advances - QTP