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  • Letter
  • Open Access

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

Carlos L. Benavides-Riveros1,2,*, Tomasz Wasak3,†, and Alessio Recati1

  • 1Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, I-38123 Trento, Italy
  • 2Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187, Dresden, Germany
  • 3Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland

  • *cl.benavidesriveros@unitn.it
  • †twasak@umk.pl
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Phys. Rev. Research 6, L012052 – Published 7 March, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L012052

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.

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Phys. Rev. Research 6, L012052– Published 7 March, 2024
  • Received 21 November 2023
  • Accepted 13 February 2024
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