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Entanglement potentials are popular measures of the nonclassicality ofsingle-mode optical fields. These potentials are defined by the amount ofentanglement (measured by, e.g., the negativity or concurrence) of the two-modefield generated by mixing a given single-mode field with the vacuum on abalanced beam splitter. We generalize this concept to define the potentials forBell nonlocality and quantum steering in specific measurement scenarios, inorder to quantify single-mode nonclassicality in a more refined way. Thus, wecan study the hierarchy of three types of potentials in close analogy to thewell-known hierarchy of the corresponding two-mode quantum correlations. Forclarity of our presentation, we focus on the analysis of the nonclassicalitypotentials for arbitrary vacuum-one-photon superpositions (VOPSs),corresponding to a photon-number qubit. We discuss experimentally feasibleimplementations for the generation of single-mode VOPS states, their mixingwith the vacuum on a balanced beam splitter, and their two-mode Wigner-functionreconstruction using homodyne tomography to determine the potentials. Weanalyze the effects of imperfections, including phase damping and unbalancedbeam splitting on the quality of the reconstructed two-mode states andnonclassicality potentials. Although we focus on the analysis of VOPS states,single-mode potentials can also be applied to study the nonclassicality ofqudits or continuous-variable systems.

Quantifying nonclassicality of vacuum-one-photon superpositions via potentials for Bell nonlocality, quantum steering, and entanglement