论文标题
最大纠缠的两Qutrit量子信息状态和De Gua的四面体定理
Maximally Entangled Two-Qutrit Quantum Information States and De Gua's Theorem for Tetrahedron
论文作者
论文摘要
研究了可分离的和纠缠的两分和两Qutrit量子信息状态之间的几何关系。为了表征两个量子状态的纠缠，我们建立了降低密度矩阵与同意之间的关系。对于邮递状态，找到并发作为平行四边形的双重面积的几何含义，对于通用量子的状态，它是由复杂的Hermitian内部产物指标的决定因素表达的，其中降低的密度矩阵与内部产物指标重合。对于通用的两Qutrit状态，对于降低的密度矩阵，我们找到了Pythagoras类型的关系，其中并发通过所有$ 2 \ times 2 $ 3 $ 3 \ TIMES3 $复杂矩阵表示表示。对于最大的纠缠两次退回状态，这种关系只是de gua的定理或毕达哥拉斯定理的三维类似物，用于三相四面体区域。讨论了我们对任意两Qudit状态的结果的概括
Geometric relations between separable and entangled two-qubit and two-qutrit quantum information states are studied. To characterize entanglement of two qubit states, we establish a relation between reduced density matrix and the concurrence. For the rebit states, the geometrical meaning of concurrence as double area of a parallelogram is found and for generic qubit states it is expressed by determinant of the complex Hermitian inner product metric, where reduced density matrix coincides with the inner product metric. In the case of generic two-qutrit state, for reduced density matrix we find Pythagoras type relation, where the concurrence is expressed by sum of all $2 \times 2$ minors of $3\times3$ complex matrix. For maximally entangled two-retrit state, this relation is just De Gua's theorem or a three-dimensional analog of the Pythagorean theorem for triorthogonal tetrahedron areas. Generalizations of our results for arbitrary two-qudit states are discussed
