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> "Like probability theory, but over the complex numbers". I'm a probability novice. How would this work? Are we talking vector fields representing multidimens
by all2 6y ago
> "Like probability theory, but over the complex numbers".
I'm a probability novice. How would this work? Are we talking vector fields representing multidimensional probabilities? Or just probabilities that happen to depend on more than one variable?
- kirrent 6y agoJust that if you have a quantum system, such as a qubit consisting of the |0> state and |1> state with a combination over the two (called a superposition) represented by a|0> + b|1> then a and b can be complex. This is in contrast to classical mechanics where, for example, pr(heads) and pr(tails) must both be real. It's only once it comes to actually making a measurement that you need to get real again.
- Y_Y 6y agoProbabilities are also always real in quantum mechanics.
- Strilanc 6y agoIt's statistics but instead of operations preserving the 1-norm (item weights [probabilities] add up to 1) they preserve the 2-norm (squared item weights [amplitudes] add up to 1). Instead of using stochastic matrices you use unitary matrices. Everything else about quantum computing follows (...with sufficient elbow grease).