A Gramian Approach to Entanglement in Bipartite Finite Dimensional\n Systems: The case of pure states

2019/12/08 by Roman Gielerak, Gielerak, Roman, Marek Sawerwain +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1912.03740

openalex publication_date 2019/12/08 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

It has been observed that the reduced density matrices of bipartite qudit\npure states possess a Gram matrix structure. This observation has opened a\npossibility of analysing the entanglement in such systems from the purely\ngeometrical point of view. In particular, a new quantitative measure of an\nentanglement of the geometrical nature, has been proposed. Using the invented\nGram matrix approach, a version of a non-linear purification of mixed states\ndescribing the system analysed has been presented.\n

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