Extracting many-body quantum resources within one-body reduced density matrix functional theory

Year: 2024

Authors: Benavides-Riveros CL., Wasak T., Recati A.

Autors Affiliation: Univ Trento, Pitaevskii BEC Ctr, CNR INO, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; Max Planck Inst Phys Komplexer Syst, Nothnitzer Str 38, D-01187 Dresden, Germany; Nicolaus Copernicus Univ Torun, Fac Phys Astron & Informat, Inst Phys, Grudziadzka 5, PL-87100 Torun, Poland.

Abstract: Quantum Fisher information (QFI) is a central concept in quantum sciences used to quantify the ultimate precision limit of parameter estimation, detect quantum phase transitions, witness genuine multipartite entanglement, or probe nonlocality. Despite this widespread range of applications, computing the QFI value of quantum many-body systems is, in general, a very demanding task. Here we combine ideas from functional theories and quantum information to develop a functional framework for the QFI of fermionic and bosonic ground states. By relying upon the constrained-search approach, we demonstrate that the QFI matrix terms can universally be determined by the one-body reduced density matrix (1-RDM), thus avoiding the use of exponentially large wave functions. Furthermore, we show that QFI functionals can be determined from the universal 1-RDM functional by calculating its derivatives with respect to the coupling strengths, thus becoming the generating functional of the QFI. We showcase our approach with the Bose-Hubbard model and present exact analytical and numerical QFI functionals. Our results provide the first connection between the one-body reduced density matrix functional theory and the quantum Fisher information.

Journal/Review: PHYSICAL REVIEW RESEARCH

Volume: 6 (1)      Pages from: L012052-1  to: L012052-7

More Information: C.L.B.-R. gratefully thanks Jerzy Cioslowski for insightful discussions and important com- ments on the manuscript. We acknowledge the European Union’s Horizon 2020 Research and Innovation program under the Marie Sklodowska-Curie Grant Agreement No. 101065295-RDMFTforbosons. This research is part of Project No. 2021/43/P/ST2/02911 cofunded by the National Science Centre and the European Union’s Horizon 2020 Research and Innovation program under the Marie Sklodowska-Curie Grant Agreement No. 945339. For the pur- pose of open access, the author has applied a CC -BY public copyright licence to any author accepted manuscript (AAM) version arising from this submission. This work has been funded from Provincia Autonoma di Trento.
KeyWords: Electron Correlation; Entanglement; Information; Entropy
DOI: 10.1103/PhysRevResearch.6.L012052

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