Suppose I have a set of 3 qubits and I have the probabilities for their distribution. This could be arbitrarily entangled or pure:
- |000> -> a
- |001> -> b
- |010> -> c
- |011> -> d
- |100> -> e
- |101> -> f
- |110> -> g
- |111> -> h
With it holding that a^2 + b^2 ... h^2 = 1.
a) Now suppose I wanted to measure the third qubit. Would it be valid to generally take the probability of the measurement being 0 as a^2 + c^2 + e^2 + g^2?
b) Assume I had measured the third qubit as 0. How would I construct a new probability distribution across my remaining 2 qubits:
- |00> -> w
- |01> -> x
- |10> -> y
- |11> -> z
Where w, x, y and z are computed from a, b ... h
Thank you in advance for any guidance you can give me!