The article discusses the properties of entanglement monotones, focusing on the logarithmic negativity and the negativity. It proves that both quantities are entanglement monotones, meaning they do not increase on average under positive partial transpose preserving (PPT) operations, which include local operations and classical communication (LOCC). This result is surprising because the logarithmic negativity is not a convex function, which is typically associated with the loss of information. The author emphasizes that convexity is a mathematical requirement for entanglement monotones and does not necessarily correspond to a physical process of information loss. The proof involves demonstrating the monotonicity of the trace norm of the partial transpose and using the concavity of the logarithm. The article also highlights the importance of continuity in this context and provides an alternative proof for the monotonicity of the negativity under LOCC operations.The article discusses the properties of entanglement monotones, focusing on the logarithmic negativity and the negativity. It proves that both quantities are entanglement monotones, meaning they do not increase on average under positive partial transpose preserving (PPT) operations, which include local operations and classical communication (LOCC). This result is surprising because the logarithmic negativity is not a convex function, which is typically associated with the loss of information. The author emphasizes that convexity is a mathematical requirement for entanglement monotones and does not necessarily correspond to a physical process of information loss. The proof involves demonstrating the monotonicity of the trace norm of the partial transpose and using the concavity of the logarithm. The article also highlights the importance of continuity in this context and provides an alternative proof for the monotonicity of the negativity under LOCC operations.