Phase-Space Inequalities Beyond Negativities

Year: 2020

Authors: Bohmann M., Agudelo E.

Autors Affiliation: INO CNR, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy; Austrian Acad Sci, Inst Quantum Opt & Quantum Informat IQOQI Vienna, Boltzmanngasse 3, A-1090 Vienna, Austria.

Abstract: We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach combines the characterization of nonclassical effects via negativities in phase-space distributions with inequality conditions usually being formulated for moments of physical observables. Importantly, the obtained criteria certify nonclassicality even when the involved phase-space distributions are non-negative. Moreover, we show how these inequalities are related to correlation measurements. The strength of the derived conditions is demonstrated by different examples, including squeezed states, lossy single-photon states, and even coherent states.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 124 (13)      Pages from: 133601-1  to: 133601-6

More Information: The authors thank Jan Sperling for stimulating discussions and Werner Vogel for helpful comments. M. B. acknowledges financial support by the Leopoldina Fellowship Programme of the German National Academy of Science (LPDS 2019-01). E. A. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie SklodowskaCurie IF (InDiQE-EU Project No. 845486).
KeyWords: Quantum-state; Nonclassical States; Squeezed States; Coherent; Entanglement; Information; Tomography; Statistics; Operators; Optics
DOI: 10.1103/PhysRevLett.124.133601

Citations: 27
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