I am reading an introduction to quantum computing and I have a question about one thing I dont understand. "In classical physics, the possible states of a system of n particles, whose individual states can be described by a vector in a two dimensional vector space, form a vector space of 2*n dimensions. However, in a quantum system the resulting state space is much larger; a system of n qubits has a state space of 2^n dimensions." Its the dimensions thing that confuses me. Lets say we have 3 classical bits of information. There are 2^3=8 possible unique configurations of these three bits, so there are 8 states. So the above asserts that these three bits have 2*3=6 dimensions, which makes sense because each bit has 2 possible states and thus there are six different numbers involved. Now consider three qubits. They apparently have 2^3=8 dimensions. Could someone explain this? And how many states do they have? I would have assumed that because of superposition they would have something like the original 8 states plus all combinations of these. Is that the right idea?