Mixed-state quantum anomalies and multipartite entanglement are explored in this paper. The study reveals a connection between mixed-state entanglement and 't Hooft anomalies, particularly in lattice systems with anomalous symmetry G. The anomaly is characterized by an invariant in group cohomology $ H^{d+2}(G,U(1)) $. The paper shows that any mixed state $ \rho $ that is strongly symmetric under G is necessarily $ (d+2) $-nonseparable, meaning it cannot be written as a mixture of tensor products of $ d+2 $ states in the Hilbert space. Furthermore, such states cannot be prepared from any $ (d+2) $-separable states using finite-depth local quantum channels, indicating long-range entanglement. The paper provides proofs for these results in $ d \leq 1 $ and plausibility arguments for $ d > 1 $. It also discusses mixed anomalies involving both strong and weak symmetries, including systems constrained by the Lieb-Schultz-Mattis type of anomaly. The anomaly-nonseparability connection allows for the generation of mixed states with nontrivial long-range multipartite entanglement. In particular, in $ d = 1 $, an example of an intrinsically mixed quantum phase is found, where states in this phase cannot be two-way connected to any pure state through finite-depth local quantum channels. The paper also discusses the implications of these results for multipartite entanglement theory, including the existence of bipartite separable but tripartite entangled states and the development of a "good" measure of multipartite entanglement for mixed states. The study highlights the importance of strong symmetry in constraining the entanglement structure of states, as opposed to weak symmetry, which has minimal constraining power. The results are applied to various examples, including the 1D cluster chain and the $ Z_2 \times Z_2 $ symmetry model, demonstrating the nonseparability and long-range entanglement of mixed states under anomalous symmetries. The paper concludes with a conjecture that $ T = \infty $ states have the least amount of entanglement possible under the symmetry constraints.Mixed-state quantum anomalies and multipartite entanglement are explored in this paper. The study reveals a connection between mixed-state entanglement and 't Hooft anomalies, particularly in lattice systems with anomalous symmetry G. The anomaly is characterized by an invariant in group cohomology $ H^{d+2}(G,U(1)) $. The paper shows that any mixed state $ \rho $ that is strongly symmetric under G is necessarily $ (d+2) $-nonseparable, meaning it cannot be written as a mixture of tensor products of $ d+2 $ states in the Hilbert space. Furthermore, such states cannot be prepared from any $ (d+2) $-separable states using finite-depth local quantum channels, indicating long-range entanglement. The paper provides proofs for these results in $ d \leq 1 $ and plausibility arguments for $ d > 1 $. It also discusses mixed anomalies involving both strong and weak symmetries, including systems constrained by the Lieb-Schultz-Mattis type of anomaly. The anomaly-nonseparability connection allows for the generation of mixed states with nontrivial long-range multipartite entanglement. In particular, in $ d = 1 $, an example of an intrinsically mixed quantum phase is found, where states in this phase cannot be two-way connected to any pure state through finite-depth local quantum channels. The paper also discusses the implications of these results for multipartite entanglement theory, including the existence of bipartite separable but tripartite entangled states and the development of a "good" measure of multipartite entanglement for mixed states. The study highlights the importance of strong symmetry in constraining the entanglement structure of states, as opposed to weak symmetry, which has minimal constraining power. The results are applied to various examples, including the 1D cluster chain and the $ Z_2 \times Z_2 $ symmetry model, demonstrating the nonseparability and long-range entanglement of mixed states under anomalous symmetries. The paper concludes with a conjecture that $ T = \infty $ states have the least amount of entanglement possible under the symmetry constraints.