2010/03/31 by Masoud Gharahi, Masoud Gharahi Ghahi, Seyed Javad Akhtarshenas
Computer Science · Physics and Astronomy · #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Qubit #quant-ph
paper · pdf · doi:10.1140/epjd/e2016-60729-1
published as Eur. Phys. J. D 70, 54 (2016) · 11 pages, 2 figures, Minor changes from previous version
openalex publication_date 2016/03/01 · arxiv created 2016/04/25 · arxiv updated 2016/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We use the concept of entangled graphs with weighted edges to present a classification for four-qubit entanglement which is based neither on the LOCC nor the SLOCC. Entangled graphs, first introduced by Plesch et al. [Phys. Rev. A 67, (2003) 012322], are structures such that each qubit of a multi-qubit system is represented as a vertex and an edge between two vertices denotes bipartite entanglement between the corresponding qubits. Our classification is based on the use of generalized Schmidt decomposition of pure states of multi-qubit systems. We show that for every possible entangled graph one can find a pure state such that the reduced entanglement of each pair, measured by concurrence, represents the weight of the corresponding edge in the graph. We also use the concept of tripartite and quadripartite concurrences as a proper measure of global entanglement of the states. In this case a circle including the graph indicates the presence of global entanglement.