The Janus State: A Universal Lower Bound for Second-Order Coherence

A single-mode squeezed vacuum is a foundational quantum state that, despite its nonclassical nature, exhibits strong, classical-like photon bunching. This feature motivates a ``quantum-of-quantum'' inquiry: can the superposition of two such states generate the opposite behavior---strong photon antibunching? We demonstrate that the ``Janus state,'' a coherent superposition of two squeezed vacua with opposing orientations, achieves exactly this. Our exact analytic solution reveals a universal lower bound on second-order coherence, proving it cannot be driven below g⁽²⁾ = 1/2. The mechanism is tuned interference that suppresses two-photon events. Beyond this asymptotic bound, we identify a practical minimum of g⁽²⁾ ≈ 0.567 at moderate squeezing, defining an accessible ``sweet spot.'' While requiring a minimal non-Gaussian element for its creation, the Janus state establishes a definitive performance limit for engineered antibunching from Gaussian resources, with a clear path toward quantum applications.