The paper explores the concept of replica topological order in quantum mixed states, which is a relatively under-explored area compared to its counterpart in pure states. The authors define two definitions for replica topological order in mixed states, involving $n$ copies of the density matrix of the mixed state. These definitions categorize topological orders in mixed states as either quantum, classical, or trivial, based on the type of information that can be encoded. For the toric code model under decoherence, the authors associate each phase with a quantum channel and describe the structure of the code space. They show that in the quantum-topological phase, a postselection-based error correction protocol can recover quantum information, while in the classical-topological phase, quantum information decoheres and cannot be fully recovered. The study uses the projected entangled pair state (PEPS) tensor network to describe the mixed state as a projected entangled pairs state (PEPS) and identifies the symmetry-protected topological order of its boundary state to the bulk topology. The findings are discussed in the context of the $n \to 1$ limit. The paper also provides examples of classical topologically ordered states using Abelian and non-Abelian lattice gauge theories and discusses the incoherent sum of loop configurations to construct CTO states. Finally, the authors classify the mixed state topological orders of the descendants of the $\mathbb{Z}_p$ toric code and demonstrate the power of the PEPS approach in simulating replica topological order for general error channels.The paper explores the concept of replica topological order in quantum mixed states, which is a relatively under-explored area compared to its counterpart in pure states. The authors define two definitions for replica topological order in mixed states, involving $n$ copies of the density matrix of the mixed state. These definitions categorize topological orders in mixed states as either quantum, classical, or trivial, based on the type of information that can be encoded. For the toric code model under decoherence, the authors associate each phase with a quantum channel and describe the structure of the code space. They show that in the quantum-topological phase, a postselection-based error correction protocol can recover quantum information, while in the classical-topological phase, quantum information decoheres and cannot be fully recovered. The study uses the projected entangled pair state (PEPS) tensor network to describe the mixed state as a projected entangled pairs state (PEPS) and identifies the symmetry-protected topological order of its boundary state to the bulk topology. The findings are discussed in the context of the $n \to 1$ limit. The paper also provides examples of classical topologically ordered states using Abelian and non-Abelian lattice gauge theories and discusses the incoherent sum of loop configurations to construct CTO states. Finally, the authors classify the mixed state topological orders of the descendants of the $\mathbb{Z}_p$ toric code and demonstrate the power of the PEPS approach in simulating replica topological order for general error channels.