Measuring nonclassicality of bosonic field quantum states via operator ordering sensitivity

Stephan de Bièvre (1, 2) , Dmitri B. Horoshko (3) , Giuseppe Patera (3) , Mikhail I. Kolobov (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 MEPHYSTO-POST - Méthodes quantitatives pour les modèles aléatoires de la physique
3 PhLAM - Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523

We introduce a new distance-based measure for the nonclassicality of the states of a bosonic field, which outperforms the existing such measures in several ways. We define for that purpose the operator ordering sensitivity of the state which evaluates the sensitivity to operator ordering of the Renyi entropy of its quasi-probabilities and which measures the oscillations in its Wigner function. Through a sharp control on the operator ordering sensitivity of classical states we obtain a precise geometric image of their location in the density matrix space allowing us to introduce a distance-based measure of nonclassicality. We analyse the link between this nonclassicality measure and a recently introduced quantum macroscopicity measure, showing how the two notions are distinct.

Keywords: Quantum Information; General Physics: Statistical and Quantum Mechanics; etc.

Domains: Quantum Physics [quant-ph]

Stephan de Bièvre, Dmitri B. Horoshko, Giuseppe Patera, Mikhail I. Kolobov. Measuring nonclassicality of bosonic field quantum states via operator ordering sensitivity. Physical Review Letters, 2019, 122 (8), pp.080402. ⟨10.1103/PhysRevLett.122.080402⟩. ⟨hal-01865597⟩