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ma18
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Homework Statement
Given a orthonormal basis of the hilbert space of qutrit states: H = span (|0>, |1>, |2>)
write in abstract notation and also a chosen consistent matrix representation, the states
a) An equiprobable quantum superposition of the three elements of the basis
b) An equiprobable incoherent ensamble of the three possible elements of the basis
c) A bipartite state which is the tensor product of the two states built in a) and b)
The Attempt at a Solution
I got the following results but I am not sure if I did it correctly so I would love it it if someone could verify them or tell what what I did wrong
The chosen matrix representation is :
|0> = (1,0,0), |1> = (0,1,0), |2> = (0,0,1)
a) 1/sqrt(3) (|0>+ |1>+ |2>)
matrix form:
1/sqrt(3) (1,1,1)
b) 1/3 (|0><0|+ |1><1|+ |2><2|)
matrix form:
1/3 (1 0 0
0 1 0
0 0 1)
c)
1/3 sqrt(3)(1 0 0
0 1 0
0 0 1
1 0 0
0 1 0
0 0 1
1 0 0
0 1 0
0 0 1)I just used wikipedia to learn about the tensor product and I applied it to the 1*3 matrix from a and the 3*3 identity matrix (multiplied by 1/3) from b. I also don't know how to do c) with an abstract representation.
Any help would be much appreciated!
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