Comment by fasterik

00, 01, 10, 11 are separable states, meaning that a pair of particles in one of those states can be described as two separate one-particle systems. For example, 01 means that the first particle is in the state 0 and the second particle is is in the state 1.

A state like (01 + 10) is not separable, so by definition it's an entangled state. "Separability" is a straightforward algebraic fact that follows from the definition of a vector and the tensor product. You can see what this means in the following Google answer

https://share.google/aimode/13jNpR7bmpPMo1pn3

(01 + 10) means that if I measure the first particle and get 0, then the second particle is now in the state 1. If I measure the first particle and get 1, then the second particle is now in the state 0.