Quantum circuits for measuring weak values, Kirkwood-Dirac quasiprobability distributions, and state spectra

Rafael Wagner, Zohar Schwartzman-Nowik, Ismael L. Paiva, Amit Te’eni, Antonio Ruiz-Molero, Rui Soares Barbosa, Eliahu Cohen, Ernesto F. Galvão

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Weak values and Kirkwood-Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory and advantages in quantum metrology. We propose simple quantum circuits to measure weak values, KD distributions, and spectra of density matrices without the need for post-selection. This is achieved by measuring unitary-invariant, relational properties of quantum states, which are functions of Bargmann invariants, the concept that underpins our unified perspective. Our circuits also enable experimental implementation of various functions of KD distributions, such as out-of-time-ordered correlators and the quantum Fisher information in post-selected parameter estimation, among others. An upshot is a unified view of nonclassicality in all those tasks. In particular, we discuss how negativity and imaginarity of Bargmann invariants relate to set coherence.

Original languageEnglish
Article number015030
JournalQuantum Science and Technology
Volume9
Issue number1
DOIs
StatePublished - Jan 2024

Bibliographical note

Publisher Copyright:
© 2024 IOP Publishing Ltd

Keywords

  • Bargmann invariants
  • Kirkwood-Dirac quasiprobability
  • nonclassicality
  • quantum circuits
  • quantum coherence
  • relational information
  • weak values

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