Enhancing quantum features and teleportation fidelity of two-mode non-Gaussian states using conditional measurements

The family of two-mode non-Gaussian entangled states, including the pair coherent states (PCSs) and their genealogies, has been extensively investigated regarding their quantum properties and their practical applications in quantum information. Specifically, certain states, such as the multiphoton catalytic pair coherent states (MCPCSs), have been newly introduced under specific experimental conditions. For a more feasible approach, in this paper, we introduce novel nonclassical states obtained by subtracting photons through conditional measurements using beam splitters applied to the two modes of the PCSs. These states are called pair coherent states with conditional measurements (PCSCMs). Our purpose is to demonstrate that the quantum features, such as entanglement, Einstein–Podolsky–Rosen (EPR) correlation, EPR steering, and the average fidelity in teleportation can be enhanced in comparison with both the original PCSs and the MCPCSs. In specific cases, several characteristics are observed in PCSCMs but not inspected in both PCSs and MCPCSs. In our findings, we prove that the quantum characteristics within the PCSCMs are influenced not just by the number of detected photons, denoted by variables k and l, but also by the discrepancy in photon numbers, especially by the difference of k − l.