Entanglement of localized states

2007/04/30 by Olivier Giraud, O. Giraud, J. Martin +3 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Anderson localization #Basis (linear algebra) #Computer science #Constant (computer programming) #Geometry #Mathematics #Physical constant #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Qubit #Statistical physics #Statistics #Value (mathematics) #Zero (linguistics) #cond-mat.mes-hall #nlin.CD #quant-ph

paper · pdf · doi:10.1103/physreva.76.042333

published as Phys. Rev. A 76, 042333 (2007) · 6 pages, 4 figures

openalex publication_date 2007/10/25 · arxiv created 2007/10/26 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We derive exact expressions for the mean value of Meyer-Wallach entanglement Q for localized random vectors drawn from various ensembles corresponding to different physical situations. For vectors localized on a randomly chosen subset of the basis, ⟨Q⟩ tends for large system sizes to a constant which depends on the participation ratio, whereas for vectors localized on adjacent basis states it goes to zero as a constant over the number of qubits. Applications to many-body systems and Anderson localization are discussed.

Citations

• Randomizing Quantum States: Constructions and Applications
• Entanglement across a transition to quantum chaos
• Superdense Coding of Quantum States
• Quantum computation of the Anderson transition in the presence of imperfections
• Remote Preparation of Quantum States
• Global entanglement in multiparticle systems

Cited by

• Growth of genuine multipartite entanglement in random unitary circuits
• Quantum state transfer in aXXchain with impurities
• Entanglement and the generation of random states in the quantum chaotic dynamics of kicked coupled tops