Quantum-Classical Boundary Engineering in Weak-to-Strong Measurements via Squeezed Vacua

Abstract: This study establishes a post-selected von Neumann framework to regulate non-classical features of single-photon-subtracted squeezed vacuum (SPSSV) and two-mode squeezed vacuum (TMSV) states during weak-to-strong measurement transitions. By synergizing Wigner-Yanase skew information, Amplitude Squared (AS) squeezing, sum squeezing, and photon statistics, we demonstrate weak value amplification as a unified control mechanism for quantum properties. Phase-space analysis via the Husimi Kano Q function reveals a critical transition: as coupling strength increases, SPSSV and TMSV states evolve from quantum non-Gaussianity to classical single-peak separability, marking a quantum-classical boundary crossing. This critical point is validated as the optimal threshold for noise suppression and signal enhancement in quantum metrology. The work provides a tunable platform for quantum sensing and weak-signal detection technologies.