Entanglement polygon inequality in qudit systems

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, Rényi entropy, and von Neumann entropy entanglement as special cases. These results provide new insights into characterizing bipartite high-dimensional entanglement in quantum information processing.

11 pages + 4 figures. Accepted in Phys. Rev. A (2022)

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• Tetrahedron genuine entanglement measure of four-qubit systems
• The polygon relation and subadditivity of entropic measures for discrete and continuous multipartite entanglement
• A Sharp Geometric Measure of Entanglement
• Unified monogamy relations for the generalized $W$-class states beyond qubits