The state you describe, sqrt(1/2) ( |01> + |10>) is an entangled state, but not all entangled states are like that. The state sqrt(1/2) ( |00> + |11> ) is also

The state you describe, sqrt(1/2) ( |01> + |10>) is an entangled state, but not all entangled states are like that. The state sqrt(1/2) ( |00> + |11> ) is also possible, and is also an entangled state, but doesn’t have the two particles in opposite states. By contrast, the state (1/2) (|00> - |01> + |10> - |11>) is (while a valid state) not an entangled state, because it is equal to (1/2) (|0> + |1>) (|0> - |1>) .