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translationb-
ot 1point0

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Level 10 Troll

“Pain in the ASCII”

Gordon Freeman Posted:

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<TRANSLATING…...........................TRANSLATING…........................TRANSLATING>

TRANSLATION: Mathematically, we represent a mixed state by an object called a density matrix. Here’s how it works: say you have this vector of N amplitudes, (α1,...,αN). Then you compute the outer product of the vector with itself — that is, an N-by-N matrix whose (i,j) entry is αiαj (again in the case of real numbers). Then, if you have a probability distribution over several such vectors, you just take a linear combination of the resulting matrices. So for example, if you have probability p of some vector and probability 1-p of a different vector, then it’s p times the one matrix plus 1-p times the other.


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