When we describe a quantum spin in terms of the basis vectors up and down, then we know that the up and down states are orthogonal to eachother. This means that they are "opposites" in the sense that if it is in the up state, we have zero probability of measuring it in the down state.
But if we have a spin in the up state, we have a 0.5 probability of measuring it in the right (or left, or in, or out) state. Then there are states with probability in between up and right.
What word do we use to denote that two states are "independent", in the sense of measuring one with probability 0.5 conditional on the other? I came up with the geometric analogy of "diagonal states".
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