Entanglement polygon inequality in qudit systems
Xue Yang, Yan‐Han Yang, Ming‐Xing Luo
Abstract
Entanglement is an important resource for quantum communication tasks. Most results are focused on qubit entanglement. Our goal in this work is to characterize the multipartite high-dimensional entanglement. We first derive an entanglement polygon inequality for the $q$ concurrence, which manifests the relationship among all the ``one-to-group'' marginal entanglements in any multipartite qudit system. This implies lower and upper bounds for the marginal entanglement of any three-qudit system. We further extend our study to general entanglement distribution inequalities for high-dimensional entanglement in terms of the unified-$(r,s)$ entropy entanglement, including Tsallis entropy, R\'enyi entropy, and von Neumann entropy entanglement as special cases. These results provide insights into characterizing bipartite high-dimensional entanglement in quantum information processing.