Suppose that two parties, Alice and Bob, would like to communicate classical information over a noisy quantum channel. Either classical or quantum information can be transmitted over a quantum channel by encoding the information in a quantum state. With this knowledge, Alice encodes the classical information that she intends to send to Bob in a (quantum) product state, as a tensor product of reduced density matrices p 1 ⊗ ⊗ p 2 ⊗ ⊗ ⋯ ⋯ where each p is diagonal and can only be used as a one time input for a particular channel ϵ ϵ .