Quasiprobabilities from incomplete and overcomplete measurements

TL;DR

This paper develops methods to reconstruct quasiprobability distributions from various measurement types, including noisy, incomplete, or overcomplete, to better identify nonclassical states in quantum systems.

Contribution

It introduces a generalized framework for constructing quasiprobabilities from diverse measurement scenarios, extending existing concepts like Kirkwood-Dirac and s-parametrized quasiprobabilities.

Findings

Effective reconstruction of quasiprobabilities from incomplete measurements.

Comparison of measurement schemes in single-qubit systems.

Enhanced criteria for identifying nonclassical states.

Abstract

We discuss the (re-)construction of quasiprobability representations from generic measurements, including noisy ones. Based on the measurement under study, quasiprobabilities and the associated concept of nonclassicality are introduced. A practical concern that we address is the treatment of informationally incomplete and overcomplete measurement scenarios, which can significantly alter the assessment of which states are deemed classical. Notions, such as Kirkwood-Dirac quasiprobabilities and s-parametrized quasiprobabilities in quantum optics, are generalized by our approach. Single-qubit systems are used to exemplify and to compare different measurement schemes, together with the resulting quasiprobabilities and set of nonclassical states.