Entanglement polygon inequality in qudit systems

• URL: http://arxiv.org/abs/2205.08801v1
• Date: Wed, 18 May 2022 08:59:18 GMT
• Title: Entanglement polygon inequality in qudit systems
• Authors: Xue Yang, Yan-Han Yang, Ming-Xing Luo
• Abstract summary: We 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. These results provide new insights into characterizing bipartite high-dimensional entanglement in quantum information processing.
• Score: 3.6720510088596297
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Entanglement is one of important resources for quantum communication tasks. Most of results are focused on qubit entanglement. Our goal in this work is to characterize the multipartite high-dimensional entanglement. We firstly 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 to general entanglement distribution inequalities for high-dimensional entanglement in terms of the unified-$(r, s)$ entropy entanglement including Tsallis entropy, R\'{e}nyi entropy, and von Neumann entropy entanglement as special cases. These results provide new insights into characterizing bipartite high-dimensional entanglement in quantum information processing.

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