3 ms·
Oh yeah, thats right.. Isn't it based on orientation in a spherical sense? I guess you could have an infinite number of those orientations.
by tzakrajs 8y ago
Oh yeah, thats right.. Isn't it based on orientation in a spherical sense? I guess you could have an infinite number of those orientations.
- whatshisface 8y agoA pure quantum state is a basis vector, written like |n>. It's called a basis vector because it shares a list of mathematical properties with the x̂,ŷ,ẑ coordinate basis vectors you might be familiar with. They can be combined, (like coordinate vectors) by writing coefficients before them. For example, 1/√2 |a> + 1/√2 |b> would be a combination of state a and state b. Combinations of states obey the condition that the sum of the squares of each coefficient equals one. This is the unitary constraint, and above you can see that 1/√2^2 + 1/√2^2 = 1/2 + 1/2 = 1. Coefficients can be complex numbers, which consist of a real part and an imaginary part. So, putting all of this together, a qbit that may be in the state |1> or the state |0> may also be in the state (a+bi)|1> + (c+di)|0>. With the unitary constraint, we can cut out a degree of freedom by introducing the equation |a+bi|^2 + |c+di|^2 = 1. This leaves three degrees of freedom, which can be mapped in to a sphere by a change of coordinates. Three spherical coordinates plus the unitary constraint specifies the four-number state combination.
- tzakrajs 8y agoVery insightful, thank you!