Colloquium

Colloquium
The geometry of concurrence as a measure of two-qubit entanglement 岩井敏洋 5月12日(金) 13時30分 It is widely recognized that concurrence can be regarded as a measure of two-qubit entanglement. This article studies the geometry of concurrence for two-qubit system to show that the concurrence is a point of the factor space $G\backslash M$, where $G=U(1)\times SU(2) \times SU(2)$ and where $M$ is the space of normalized two-qubit states. Any monotonically increasing function of the concurrence, for example, the von Neumenn entropy, can serve as a measure for entanglement. From the viewpoint of Riemannian geometry, a state with concurrence $r$ is distant from the separable states by $(\sin^{-1}r)/\sqrt{2}$ with $0\leq r \leq 1$.

The geometry of concurrence as a measure of two-qubit entanglement

岩井敏洋

5月12日(金) 13時30分

It is widely recognized that concurrence can be regarded as a measure of two-qubit entanglement. This article studies the geometry of concurrence for two-qubit system to show that the concurrence is a point of the factor space $G\backslash M$, where $G=U(1)\times SU(2) \times SU(2)$ and where $M$ is the space of normalized two-qubit states. Any monotonically increasing function of the concurrence, for example, the von Neumenn entropy, can serve as a measure for entanglement. From the viewpoint of Riemannian geometry, a state with concurrence $r$ is distant from the separable states by $(\sin^{-1}r)/\sqrt{2}$ with $0\leq r \leq 1$.