I'm having a little bit of trouble getting my head around the idea of the reduced density operator being used to tell us about the entanglement of a state. I understand that if you take the reduced density operator of any of the Bell states, you get a reduced density operator proportional to the identity, and this is defined as being a maximally entangled state. But why is this a proof that the state is entangled? I have written problem that asks to solve the reduced density operator for a particular state. I solve for the reduced density operator and I get a 2x2 matrix with elements in each slot. It satisfies the conditions to be a density operator, but what does it tell me about the entanglement of the state? Any clarification would be much appreciated!