Interferometry of quantum correlation functions to access quasiprobability distribution of work

The Kirkwood-Dirac quasiprobability distribution emerges from the quantum correlation function of two observables measured at distinct times and is therefore relevant for fundamental physics and quantum technologies. These quasiprobabilities follow all but one of Kolmogorov axioms for joint probabil...

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Published inarXiv.org
Main Authors Hernández-Gómez, Santiago, Isogawa, Takuya, Belenchia, Alessio, Levy, Amikam, Fabbri, Nicole, Gherardini, Stefano, Cappellaro, Paola
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.05.2024
Subjects
Axioms
Characteristic functions
Correlation
Electron spin
Hamiltonian functions
Interferometry
Nuclear spin
Uncertainty
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Summary:The Kirkwood-Dirac quasiprobability distribution emerges from the quantum correlation function of two observables measured at distinct times and is therefore relevant for fundamental physics and quantum technologies. These quasiprobabilities follow all but one of Kolmogorov axioms for joint probability distributions: they can take non-positive values. Their experimental reconstruction becomes challenging when expectation values of incompatible observables are involved. Previous strategies aimed to reconstruct them using weak measurements or combining strong measurements. Here, we use a more direct approach, an interferometric scheme aided by an auxiliary system, to reconstruct the Kirkwood-Dirac quasiprobability distribution. We experimentally demonstrate the interferometric scheme in an electron-nuclear spin system associated with a nitrogen-vacancy center in diamond. By measuring the characteristic function, we reconstruct the quasiprobability distribution of the work and analyze the behavior of the first and second moments of work. Our results clarify the physical meaning of the work quasiprobability distribution in the context of quantum thermodynamics. Finally, having measured the real and imaginary parts of the Kirkwood-Dirac quasiprobability of work, we are also able to study the uncertainty of measuring the Hamiltonian of the system at two times, via the Robertson-Schr{\"o}dinger uncertainty relation, for different initial states.
ISSN:2331-8422