2024/12/07 by Joydeep Naskar, Anonymous, Sai Satyam Samal +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Holography #Inequality #Joint quantum entropy #Mathematical analysis #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum discord #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum relative entropy #Statistical physics #Theoretical physics #Topological entropy in physics
paper · pdf · doi:10.1103/hvf8-jcff
published in Physical review. D/Physical review. D. 114(2) (American Physical Society)
openalex publication_date 2026/06/25 · openalex created_date 2026/06/26 · openalex updated_date 2026/07/18
Topological entanglement entropy (TEE) is an efficient way to detect topological order in the ground state of gapped Hamiltonians. The seminal work of Kitaev and Preskill~\citepreskill-kitaev-tee and simultaneously by Levin and Wen~\citelevin-wen-tee proposed information quantities that can probe the TEE. In the present work, we explain why the subtraction schemes in the proposed information quantities~\citelevin-wen-tee,preskill-kitaev-tee work for the computation of TEE and generalize them for arbitrary number of subregions by explicitly noting the necessary conditions for an information quantity to capture TEE. Our conditions differentiate the probes defined by Kitaev-Preskill and Levin-Wen into separate classes. While there are infinitely many possible probes of TEE, we focus particularly on the cyclic quantities Q2n+1 and multi-information In. We also show that the holographic entropy inequalities are satisfied by the quantum entanglement entropy of the non-degenerate ground state of a topologically ordered two-dimensional medium with a mass gap.