Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables

Year: 2023

Authors: Lostaglio M., Belenchia A., Levy A., Hernbndez-Gumez S., Fabbri N., Gherardini S.

Autors Affiliation: Univ Amsterdam, Korteweg de Vries Inst Math & QuSoft, Amsterdam, Netherlands; Eberhard Karls Univ Tubingen, Inst Theoret Phys, D-72076 Tubingen, Germany; Queens Univ Belfast, Ctr Theoret Atom Mol & Opt Phys, Sch Math & Phys, Belfast BT7 1NN, North Ireland; Bar Ilan Univ, Dept Chem, IL-52900 Ramat Gan, Israel; Bar Ilan Univ, Ctr Quantum Entanglement Sci & Technol, IL-52900 Ramat Gan, Israel; Univ Firenze, European Lab Nonlinear Spect LENS, I-50019 Sesto Fiorentino, Italy; Univ Firenze, Dipartimento Fis & Astron, I-50019 Sesto Fiorentino, Italy; Consiglio Nazl Ric CNR INO, Ist Nazl Ott, I-50019 Sesto Fiorentino, Italy; Consiglio Nazl Ric CNR INO, Ist Nazl Ott, Area Sci Pk, I-34149 Trieste, Italy

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.

Journal/Review: QUANTUM

Volume: 7      Pages from: 1128-1  to: 1128-35

More Information: 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.Hernandez-Gomez acknowledges financial support from CNR-FOE-LENS-2020. S. Gherardini acknowledges The Blanceflor Foundation for financial support through the project The the Rmodynamics 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.r and and by the European Union’s Next Gen-eration EU Programme with the I-PHOQS In-frastructure [IR0000016, ID D2B8D520, CUP B53C22001750006] Integrated infrastructure ini-tiative in Photonic and Quantum Sciences.
KeyWords: Wigner-function; Irreversible Processes; Mechanical Theory; Quantum; Disturbance; Equality; Echoes; Error
DOI: 10.22331/q-2023-10-09-1128

Citations: 20
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