论文标题
三个Qubits的纠缠纠缠纠缠和冯·诺伊曼熵之间的关系
A relation among tangle, 3-tangle, and von Neumann entropy of entanglement for three qubits
论文作者
论文摘要
在本文中，我们得出了三个量子位的纯状态缠结的一般公式，并呈现了三个明确的局部统一（LU）多项式不变性。我们的结果超出了纠缠，三角和von Neumann的经典作品，用于Ac \'ın等人的纠缠。通过连接ASD的缠结，3键和von Neumann熵的施密特分解（ASD）与Ac \'ın等人的lu不变式连接。特别是，我们的结果揭示了缠结，三角和冯·诺伊曼熵之间的一般关系，以及平均值之间的关系。这些关系可以帮助我们找到满足纠缠，三角和冯·诺伊曼熵的不同要求的纠缠状态。此外，我们获得了三个量子位的所有状态，其中缠结，同意，三角和von Neumann熵不会消失，并且当三个量子位之一被追踪时，这些状态可以持久。我们指出，对于三Q量W状态，其平均von Neumann熵仅在W SLOCC类中是最大的，并且在ASD下，三倍的GHz状态是独特的状态，其通过追踪任何两个Qubits获得的降低密度算子具有最大的Von Neumann Neumann Neumann熵。
In this paper, we derive a general formula of the tangle for pure states of three qubits, and present three explicit local unitary (LU) polynomial invariants. Our result goes beyond the classical work of tangle, 3-tangle and von Neumann entropy of entanglement for Ac\'ın et al.' Schmidt decomposition (ASD) of three qubits by connecting the tangle, 3-tangle, and von Neumann entropy for ASD with Ac\'ın et al.'s LU invariants. In particular, our result reveals a general relation among tangle, 3-tangle, and von Neumann entropy, together with a relation among their averages. The relations can help us find the entangled states satisfying distinct requirements for tangle, 3-tangle, and von Neumann entropy. Moreover, we obtain all the states of three qubits of which tangles, concurrence, 3-tangle and von Neumann entropy don't vanish and these states are endurable when one of three qubits is traced out. We indicate that for the three-qubit W state, its average von Neumann entropy is maximal only within the W SLOCC class, and that under ASD the three-qubit GHZ state is the unique state of which the reduced density operator obtained by tracing any two qubits has the maximal von Neumann entropy.
