Entanglement measures based on observable correlations

Florian Mintert, Stephen Walburn, P. H. Souto Ribeiro +2 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.

F. Mintert

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.

Masato Koashi, Andreas Winter

It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the ``monogamous nature of entanglement.'' In this paper we present a simple identity which captures the trade off between entanglement and classical correlation, which can be used to derive rigorous monogamy relations. We also prove various other trade offs of a monogamy nature for other entanglement measures and secret and total correlation measures.

Florian Mintert