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

TL;DR

This paper introduces generalized measures called potentials for Bell nonlocality and quantum steering to quantify the nonclassicality of vacuum-one-photon superpositions, extending traditional entanglement potentials, with experimental feasibility and robustness analysis.

Contribution

It generalizes entanglement potentials to include Bell nonlocality and quantum steering, providing a refined hierarchy of nonclassicality measures for single-mode states.

Findings

Defined potentials for Bell nonlocality and steering for VOPS states

Analyzed effects of imperfections on nonclassicality potentials

Proposed feasible experimental implementations

Abstract

Entanglement potentials are popular measures of the nonclassicality of single-mode optical fields. These potentials are defined by the amount of entanglement (measured by, e.g., the negativity or concurrence) of the two-mode field generated by mixing a given single-mode field with the vacuum on a balanced beam splitter. We generalize this concept to define the potentials for Bell nonlocality and quantum steering in specific measurement scenarios, in order to quantify single-mode nonclassicality in a more refined way. Thus, we can study the hierarchy of three types of potentials in close analogy to the well-known hierarchy of the corresponding two-mode quantum correlations. For clarity of our presentation, we focus on the analysis of the nonclassicality potentials for arbitrary vacuum-one-photon superpositions (VOPSs), corresponding to a photon-number qubit. We discuss experimentally feasible implementations for the generation of single-mode VOPS states, their mixing with the vacuum on a balanced beam splitter, and their two-mode Wigner-function reconstruction using homodyne tomography to determine the potentials. We analyze the effects of imperfections, including phase damping and unbalanced beam splitting on the quality of the reconstructed two-mode states and nonclassicality potentials. Although we focus on the analysis of VOPS states, single-mode potentials can also be applied to study the nonclassicality of qudits or continuous-variable systems.