Goddammit El Reg
It NEVER comes out right, does it?
Instead of two states, 0 and 1, however, a qubit can occupy an infinite number of states as its quantum states are entangled with one another.
NO!
The qubit is in a superposition of states, a bit of 0, a bit of 1 (written as nonmixable vectors |0> and |1>):
Q = a * |0> + b * |1>
...where a and b are complex values and the vector <a,b> is of length 1 (i.e. on the complex sphere of complex dimension 2)
This is mathematically analoguos to bog-standard "I don't know" probability, where a classical system is in some unknown state until we look (but in QM, the system is ACTUALLY in the superposition until we look):
Q = a * |0> + b * |1>
where a and b are real values and the vector <a,b> is of length 1 (i.e. on the unit circle on the real plane)
The ENTANGLEMENT comes from composing N qbits into an entangled whole, and the state of the system is then described by 2^N complex values, one for each "classical state", anmd the 2^N complex vector is on the 2^N-dimensional complex unit sphere. For example, for 2 qubits:
QQ = a * |00> + b * |01> + c * |10> + d * |11>
One can mix-in to "QM probability" above some classical "don't know" probability to obtain "mixtures". For example, we have system QQ which we know is in state QQ1 with classical probability p, and in state QQ2 with classical probability (1-p), then:
QQ = p * QQ1 + (1-p) * QQ2
...some people dispute that such mixtures have physical reality though as they are indistinguishable from a quantum state.