Quantifying Quantum Entanglement in Two-Qubit Mixed State from Connected Correlator

Animesh Datta, Steven T. Flammia, Carlton M. Caves +1 more

Xingyu Guo, Chen‐Te Ma

Our study employs a connected correlation matrix to quantify quantum entanglement. The matrix encompasses all necessary measures for assessing the degree of entanglement between particles. We begin with a three-qubit state and involve obtaining a mixed state by performing partial tracing over one qubit. Our goal is to exclude the non-connected sector by focusing on the connected correlation. This suggests that the connected correlation is deemed crucial for capturing relevant entanglement degrees. The study classifies mixed states and observes that separable states exhibit the lowest correlation within each class. We demonstrate that the entanglement measure monotonically increases concerning the correlation measure. This implies that connected correlation serves as an effective measure of quantum entanglement. Finally, our proposal suggests that interpreting quantum entanglement from a local perspective is possible. The observable is described as a vector with locality but violates freedom of choice.

Xingyu Guo, Chen‐Te Ma

Our study employs a connected correlation matrix to quantify Quantum Entanglement. The matrix encompasses all necessary measures for assessing the degree of entanglement between particles. We begin with a three-qubit state and involve obtaining a mixed state by performing partial tracing over one qubit. Our goal is to exclude the non-connected sector by focusing on the connected correlation. This suggests that the connected correlation is deemed crucial for capturing relevant entanglement degrees. The study classifies mixed states and observes that separable states exhibit the lowest correlation within each class. We demonstrate that the entanglement measure monotonically increases concerning the correlation measure. This implies that connected correlation serves as an effective measure of Quantum Entanglement. Finally, our proposal suggests that interpreting Quantum Entanglement from a local perspective is possible. The observable is described as a vector with locality but violates freedom of choice.

Fa Zhao, Dong Wang, Ye Liu

최정운

Jens Eisert, H. J. Briegel

We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on the full state space and is shown to be an entanglement monotone, that is, it cannot increase under local quantum operations with classical communication and under mixing. For a large class of mixed states this measure of entanglement can be calculated exactly, and it provides a detailed classification of mixed states. We also present a connection to the best separable approximation of an entangled state of a two-qubit system.