2006/06/30 by Spyridon Michalakis, Bruno Nachtergaele · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Conjecture #Entanglement witness #Mathematical physics #Mathematics #Matrix product state #Multipartite entanglement #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Spins #Squashed entanglement #math-ph #math.MP #msc:82B20 #msc:94A99 #quant-ph
paper · pdf · doi:10.1103/physrevlett.97.140601
published as Phys. Rev. Lett. 97 (2006) 140601 · PACS 03.67.Mn, 05.50.+q. Minor typos in v1 corrected. In v2: expanded Introduction and Discussion. Simplified proof of the main result
arxiv created 2006/07/17 · openalex publication_date 2006/10/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider entanglement properties of pure finitely correlated states (FCS). We derive bounds for the entanglement of a spin with an interval of spins in an arbitrary pure FCS. Finitely correlated states are also known as matrix product states or generalized valence-bond states. The bounds become exact in the case where one considers the entanglement of a single spin with a half-infinite chain to the right of it. Our bounds provide a proof of the recent conjecture by Benatti, Hiesmayr, and Narnhofer that their necessary condition for nonvanishing entanglement in terms of a single spin and the memory of the FCS is also sufficient. We also generalize the study of entanglement in the Affleck-Kennedy-Lieb-Tasaki model by Fan, Korepin, and Roychowdhury. Our result permits a more efficient calculation, numerically and in some cases analytically, of the entanglement of arbitrary finitely correlated quantum spin chains.