Entropy of entanglement and multifractal exponents for random states

2008/07/23 by Olivier Giraud, John Martin, Bertrand Georgeot
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems #quant-ph

paper · pdf · doi:10.1103/physreva.79.032308

published as Phys. Rev. A 79, 032308 (2009) · 5 pages, 2 figures

arxiv created 2008/07/23 · openalex publication_date 2009/03/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We relate the entropy of entanglement of ensembles of random vectors to their generalized fractal dimensions. Expanding the von Neumann entropy around its maximum we show that the first order only depends on the participation ratio, while higher orders involve other multifractal exponents. These results can be applied to entanglement behavior near the Anderson transition.

Citations

• Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective
• Entanglement in disordered systems at criticality
• Quantum computation of the Anderson transition in the presence of imperfections
• Entanglement in many-body systems