Photon-Conditioned Squeezed States for Directional Displacement Response in Continuous-Variable Photonics

Squeezed Fock states, photon-subtracted squeezed states, and optical cat states are established non-Gaussian resources in continuous-variable quantum optics. Here we compare these known state families from a task-oriented perspective: matched mean photon number, scalar Wigner negativity, and directional displacement-fidelity response. Starting from squeezed vacuum, single-photon subtraction prepares a state proportional to \(S(r,\theta)\ket{1}\), while two-photon subtraction prepares an even-parity squeezed Fock superposition rather than a pure \(S(r,\theta)\ket{2}\). We benchmark photon-conditioned squeezed states against Fock and coherent-cat references using the integrated Wigner negativity \(\delta\), the energy-normalized metric \(\delta/\langle n\rangle\), and fidelity-threshold displacement radii \(R_F(\phi)\). Cat benchmarks remain strong scalar Wigner-negativity resources, whereas photon-conditioned squeezed states provide an origin-centered alternative with tunable anisotropic displacement response. In particular, the two-photon-subtracted squeezed state shows favorable displacement-fidelity radii over selected quadrature directions at matched \(\langle n\rangle\). These results identify a regime relevant to homodyne-aligned continuous-variable control and anisotropic displacement-noise mitigation, with directional sensing as a natural dual application.