Entanglement, Squeezing and non-Locality in Filtered Two-Mode Squeezed Mixed States

We investigate the entanglement and non-locality between specific spectral components of continuous variable two-mode squeezed mixed states, identifying their limits. These spectral components are selected from output modes using filters commonly employed in optomechanical systems. Both entanglement and non-locality reach their peak when the filters are identical. However, increasing the degree of input squeezing while applying non-identical filters disrupts both entanglement and non-locality, leading to a bell-shaped pattern. Additionally, we provide precise boundaries for entanglement and non-locality. Furthermore, we also evaluate the squeezing of two-mode hybrid quadrature as a measure of entanglement, thereby demonstrating how it remains analogous to logarithmic negativity. Combined with the filter, the population of two-mode squeezed thermal light influences the angle of a maximally squeezed hybrid quadrature.