Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables

Matteo Lostaglio, Alessio Belenchia, Amikam Levy, Santiago Hernández-Gómez, Nicole Fabbri, Stefano Gherardini

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Abstract

Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to properly account for non-classical features in the context of condensed matter physics (scrambling, dynamical phase transitions) metrology (standard and post-selected), thermodynamics (power output and fluctuation theorems), foundations (contextuality, anomalous weak values) and more. Given the growing relevance of the KDQ across the quantum sciences, our aim is two-fold: First, we highlight the role played by quasiprobabilities in characterizing the statistics of quantum observables and processes in the presence of measurement incompatibility. In this way, we show how the KDQ naturally underpins and unifies quantum correlators, quantum currents, Loschmidt echoes, and weak values. Second, we provide novel theoretical and experimental perspectives by discussing a wide variety of schemes to access the KDQ and its non-classicality features.

Original languageEnglish
JournalQuantum
Volume7
DOIs
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© Quantum.All rights reserved.

Funding

We would like to thank the two Referees for the many suggestions that have helped us improving our manuscript. Special thank goes to the anynomous Referee A for suggesting substantial improvements for the proof of some of the results in our work, in particular a simpler proof of Lemma 1.1. A. Belenchia acknowledges support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) project number BR 5221/4-1. A. Levy acknowledges support from the Israel Science Foundation (Grant No. 1364/21). S. Hernández-Gómez acknowledges financial support from CNR-FOE-LENS-2020. S. Gherardini acknowledges The Blanceflor Foundation for financial support through the project “The theRmodynamics behInd thE meaSuremenT postulate of quantum mEchanics (TRIESTE)”, and the MISTI Global Seed Funds MIT-FVG Collaboration Grant “Non-Equilibrium Thermodynamics of Dissipative Quantum Systems (NETDQS)”. The work was also supported by the European Commission under GA n. 101070546-MUQUABIS, the PNRR MUR project PE0000023-NQSTI, and and by the European Union's Next Generation EU Programme with the I-PHOQS Infrastructure [IR0000016, ID D2B8D520, CUP B53C22001750006] “Integrated infrastructure initiative in Photonic and Quantum Sciences”. We would like to thank the two Referees for the many suggestions that have helped us improving our manuscript. Special thank goes to the anynomous Referee A for suggesting substantial improvements for the proof of some of the results in our work, in particular a simpler proof of Lemma 1.1. A. Belenchia acknowledges support from the Deutsche Forschungs-gemeinschaft (DFG, German Research Foundation) project number BR 5221/4-1. A. Levy acknowledges support from the Israel Science Foundation (Grant No. 1364/21). S. Hernández-Gómez acknowledges financial support from CNR-FOE-LENS-2020. S. Gherardini acknowledges The Blanceflor Foundation for financial support through the project “The theRmodynamics behInd thE meaSuremenT postulate of quantum mEchanics (TRIESTE)”, and the MISTI Global Seed Funds MIT-FVG Collaboration Grant “Non-Equilibrium Thermodynamics of Dissipative Quantum Systems (NETDQS)”. The work was also supported by the European Commission under GA n. 101070546–MUQUABIS, the PNRR MUR project PE0000023-NQSTI, and and by the European Union’s Next Generation EU Programme with the I-PHOQS Infrastructure [IR0000016, ID D2B8D520, CUP B53C22001750006] “Integrated infrastructure initiative in Photonic and Quantum Sciences”.

FundersFunder number
Blanceflor Foundation
CNR-FOE-LENS-2020
MISTI
MUQUABISCUP B53C22001750006, PE0000023-NQSTI, IR0000016, D2B8D520
PNRR
European Commission101070546
Deutsche ForschungsgemeinschaftBR 5221/4-1
Israel Science Foundation1364/21

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