The paper by R. Simon explores the Peres-Horodecki criterion for separability in continuous variable systems. The partial transpose operation, which is geometrically interpreted as mirror reflection in phase space, is shown to impose stronger uncertainty principles on separable states compared to traditional ones. For bipartite Gaussian states, the Peres-Horodecki criterion is proven to be both necessary and sufficient for separability. The author demonstrates that the criterion can be simplified and applied directly to the variance matrix of a state, without the need to transform it into a specific form. The paper also discusses the implications of the criterion for the second moments of states and provides a proof for the separability of Gaussian states using the criterion. Additionally, the author notes that the geometric interpretation of the partial transpose as mirror reflection holds for other quasi-probability distributions and highlights the practical advantages of the Peres-Horodecki criterion over other approaches.The paper by R. Simon explores the Peres-Horodecki criterion for separability in continuous variable systems. The partial transpose operation, which is geometrically interpreted as mirror reflection in phase space, is shown to impose stronger uncertainty principles on separable states compared to traditional ones. For bipartite Gaussian states, the Peres-Horodecki criterion is proven to be both necessary and sufficient for separability. The author demonstrates that the criterion can be simplified and applied directly to the variance matrix of a state, without the need to transform it into a specific form. The paper also discusses the implications of the criterion for the second moments of states and provides a proof for the separability of Gaussian states using the criterion. Additionally, the author notes that the geometric interpretation of the partial transpose as mirror reflection holds for other quasi-probability distributions and highlights the practical advantages of the Peres-Horodecki criterion over other approaches.