Quantum Rényi entropy by optimal thermodynamic integration paths

Miha Srdinšek (1, 2, 3) , Michele Casula (2) , Rodolphe Vuilleumier (3)

1 ISCD - Institut des Sciences du Calcul et des Données
2 IMPMC_TQM - Théorie quantique des matériaux [IMPMC]
3 PASTEUR - Processus d'Activation Sélective par Transfert d'Energie Uni-électronique ou Radiatif (UMR 8640)

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.

Domaines: Physique Quantique [quant-ph]

Miha Srdinšek, Michele Casula, Rodolphe Vuilleumier. Quantum Rényi entropy by optimal thermodynamic integration paths. Physical Review Research, 2022, 4 (3), pp.L032002. ⟨10.1103/PhysRevResearch.4.L032002⟩. ⟨hal-03779480⟩