Faithful quantumness certification for single-mode continuous-variable systems

Develop a quantumness certification functional for one-dimensional continuous-variable (single-mode) quantum states that is faithfully discriminating, meaning it always detects and certifies every nonclassical state and certifies only classical states as classical. In phase-space terms, ensure the functional attains negative values somewhere for every nonclassical state and remains nonnegative for all classical states, providing a universally applicable method for both theoretical and experimentally reconstructed states.

Background

The paper studies phase-space-based certification of nonclassicality for one-dimensional continuous-variable systems. While the Sudarshan-Glauber P distribution provides a definition of nonclassicality via negativity, it is typically too singular to reconstruct or analyze in practice. Bohmann and Agudelo’s functional xi(x,p) was shown to be sufficient: xi(x,p) < 0 implies nonclassicality, but it is not necessary, leading to failures on weakly nonclassical states.

This work generalizes xi to a new family of certification functionals S(T,ΔT) that can be more sensitive, yet both xi and S fail for very weakly nonclassical states. Consequently, a universally faithful certification—one that necessarily detects all nonclassical states and never mislabels them as classical—remains unresolved.