The interesting emergent phenomenon, however, is that all four states exist probabilistically, at the same time, requiring four new coefficients, instead of just the independent coefficients, in order to represent this system.
For example, a classical two-bit system contains four states: 00, 01, 10, and 11. The specific state of the four states can be defined using only two values: the two bits that define it. Again, quantum mechanics is not so simple. A two-qubit quantum entangled system can have four states, just like the classical system. The interesting emergent phenomenon, however, is that all four states exist probabilistically, at the same time, requiring four new coefficients, instead of just the independent coefficients, in order to represent this system. Going further, for N qubits, 2N coefficients are required to be specified, so to simulate just 300 entangled qubits, the number of coefficients would be greater than that of the number of atoms in the known universe.