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  • Letter
  • Open Access

Quantum Rényi entropy by optimal thermodynamic integration paths

Miha Srdinšek1,2,3,*, Michele Casula2, and Rodolphe Vuilleumier3

  • 1Institut des sciences du calcul et des données (ISCD), Sorbonne Université, 4 Place Jussieu, 75005 Paris, France
  • 2Institut de minéralogie, de physique des matériaux et de cosmochimie (IMPMC), Sorbonne Université, CNRS UMR 7590, MNHM, 4 Place Jussieu, 75005 Paris, France
  • 3Processus d'Activation Sélectif par Transfert d'Energie Uni-électronique ou Radiative (PASTEUR), CNRS UMR 8640, Département de Chimie, École Normale Superieure, 24 rue Lhomond, 75005 Paris, France

  • *miha.srdinsek@upmc.fr
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Phys. Rev. Research 4, L032002 – Published 5 July, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L032002

Abstract

Despite being a well-established operational approach to quantify entanglement, Rényi entropy calculations have been plagued by their computational complexity. We introduce here a theoretical framework based on an optimal thermodynamic integration scheme, where the Rényi entropy can be efficiently evaluated using regularizing paths. This approach avoids slowly convergent fluctuating contributions and leads to low-variance estimates. In this way, large system sizes and high levels of entanglement in model or first-principles Hamiltonians are within our reach. We demonstrate this approach in the one-dimensional quantum Ising model and perform an evaluation of entanglement entropy in the formic acid dimer, by discovering that its two shared protons are entangled even above room temperature.

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Phys. Rev. Research 4, L032002– Published 5 July, 2022
  • Received 29 December 2021
  • Accepted 9 June 2022
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