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 language | English |
|---|---|
| Article number | 015030 |
| Journal | Quantum Science and Technology |
| Volume | 9 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2024 |
Bibliographical note
Publisher Copyright:© 2024 IOP Publishing Ltd
Funding
We thank the International Iberian Nanotechnology Laboratory (INL) and the Bar-Ilan Institute of Nanotechnology and Advanced Materials for their support, which was instrumental in kick-starting this collaboration. R W and A R M acknowledge support from FCT—Fundação para a Ciência e a Tecnologia (Portugal) through PhD Grants SFRH/BD/151199/2021 and SFRH/BD/151453/2021, respectively. R S B and E F G also acknowledge support from FCT, CEECINST/00062/2018. I L P acknowledges support from the ERC Advanced Grant FLQuant. The work of the INL-based authors (R W, A R M, R S B, E F G) was supported by the Digital Horizon Europe Project FoQaCiA, GA No. 101070558. E C was supported by the Israeli Innovation Authority under Project 73795 and the Eureka project, by Elta Systems Ltd by the Pazy Foundation, by the Israeli Ministry of Science and Technology, and by the Quantum Science and Technology Program of the Israeli Council of Higher Education.
| Funders | Funder number |
|---|---|
| Digital Horizon Europe Project FoQaCiA | 101070558 |
| Quantum Science and Technology Program of the Israeli Council of Higher Education | |
| European Commission | |
| Fundação para a Ciência e a Tecnologia | SFRH/BD/151453/2021, SFRH/BD/151199/2021, CEECINST/00062/2018 |
| Ministry of science and technology, Israel | |
| Israel Innovation Authority | 73795 |
Keywords
- Bargmann invariants
- Kirkwood-Dirac quasiprobability
- nonclassicality
- quantum circuits
- quantum coherence
- relational information
- weak values