I'm not quite sure I understand your question, but maybe it will make more sense if I explain what the equations mean.
My earlier example just came out of analyzing a system with two qubits. Qubits are quantum bits: they take 0 or 1 values like normal bits, but live in-between the two in quantum neverland (superposition is the technical term) until you make a measurement. At that point they wind up turning into either 0 or 1. Opinions are divided about what exactly is happening here - the Copenhagen interpretation of QM holds that the measurement causes the wavefunction to collapse, and the qubit takes one of the two states. The many-worlds interpretation holds that it becomes both 0 and 1, but each outcome takes place in a distinct parallel universe, so you only see one of them, and presumably your counterpart in the other universe sees the opposite outcome. This is actually serious physics, and as you might imagine, it's a goldmine for science fiction authors.
Usually people identify these 0/1 values with the spin of a particle - this is a quantum number that is either 'up' or 'down', and you can assign 0 and 1 to either one of those. It doesn't have to be spin though - it could be some other property. The math doesn't care, it just abstracts away those details to leave you 0 and 1, since the physical realization of the system is irrelevant.
So now if you say that the state of a single qubit is (|0> + |1>)/sqrt(2), this is the mathematical version of saying that the qubit is in a 50-50 superposition between 0 and 1. If you measure it, the spin will be up half the time, and down the other half of the time. A simpler case is if the state is just |0> - then you'll always get the same measurement 100% of the time.
Now if we take both these qubits as a single system, the state of the entire system is described by the tensor product of the two component states: |0>(|0> + |1>)/sqrt(2), which can also be written as (|00> + |01>)/sqrt(2). If something like this pops out at the end of your analysis of some fancy two-qubit system, then you know you have two qubits where the first is always 0, and the other is 0 half the time, and 1 otherwise. If you look at the version where I multiplied it out, it's basically saying that half the time you have (0, 0), and the other half you have (0, 1). Slightly different way of looking at the same thing, but you see that you can separate the two qubits. They don't imply anything about each other's states - the first one is always 0, regardless of the other guy, which is basically just a coin toss. In other words, you can decompose the system, or 'disentangle' it, if you prefer.
On the other hand, if your analysis produces something like (|00> + |11>)/sqrt(2), it's saying that you have (0, 0) half the time, and (1, 1) the other half. Notice now that you can't decompose the state. If the first qubit is 1, the second has to be 1 as well. The system is unable to produce any states where the two bits have different values. Because knowing one bit instantly gives you the value of the other, without having to bother with the actual measurement, you've got entanglement.
Hopefully I remember this right, or maybe a real physicist will turn up and "laugh the blue off my ass".
Modifié par abstractwhiz, 11 avril 2010 - 07:51 .





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