2014/06/02 by Andreas Osterloh
Computer Science · Mathematics · Physics and Astronomy · #Dimension (graph theory) #Extension (predicate logic) #Generalization #Hilbert space #Multipartite #Multipartite entanglement #Product (mathematics) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum many-body systems #State (computer science) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/47/49/495301
published as J. Phys. A 47, 495301 (2014) · 8 pages, revtex4. arXiv admin note: text overlap with arXiv:1309.6235
arxiv created 2014/06/02 · openalex publication_date 2014/11/12 · arxiv updated 2016/06/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
I generalize the concept of balancedness to qudits with arbitrary dimension d . It is an extension of the concept of balancedness by Osterloh and Siewert (2010 New J. Phys. 12 075025 ). At first, I define maximally entangled states as being the stochastic states (with local reduced density matrices for a d -dimensional local Hilbert space) that are not product states and show that every so-defined maximal genuinely multi-qudit entangled state is balanced. Furthermore, all irreducibly balanced states are genuinely multi-qudit entangled and are locally equivalent with respect to SL( d ) transformations (i.e. the local filtering transformations) to a maximally entangled state. In particular the concept given here gives a condition that all maximal genuinely multi-qudit entangled states for general local Hilbert space dimension d have to satisfy. A general genuinely multi-qudit entangled state is an element of the partly balanced SU( d )-orbits.