2. Reduced GHZ Consider the n-qubit "Schrdinger cat state" (or "generalized GHZ state) 10.0)+11 ... 1) 1 2 a) [3 Points) What probability distribution over n-bit strings do we observe if we Hadamard the first n - 1 qubits, then measure all n qubits in the {10), (1)} basis? Show your work. Your answer should show that the string 00...000 is observed with probability ?, the string 00...001 is observed with probability ??, etc. You should be able to give a succinct answer. b) [3 Points) What probability distribution do we observe if we take the similar-looking state 10...0) (0...01 + 11 ... 1) (1...1! 2 apply Hadamards to the first n - 1 qubits, and then measure all n qubits in the {10),|1}} basis? Is this the same distribution or a different one than in part (a) and what did you expect? Show your work. C) (2 Points] What probability distribution over n-bit strings do we observe if we Hadamard all n qubits of the state from part (a), then measure all n qubits in the {10), 11)} basis? Show your work. 2. Reduced GHZ Consider the n-qubit "Schrdinger cat state" (or "generalized GHZ state) 10.0)+11 ... 1) 1 2 a) [3 Points) What probability distribution over n-bit strings do we observe if we Hadamard the first n - 1 qubits, then measure all n qubits in the {10), (1)} basis? Show your work. Your answer should show that the string 00...000 is observed with probability ?, the string 00...001 is observed with probability ??, etc. You should be able to give a succinct answer. b) [3 Points) What probability distribution do we observe if we take the similar-looking state 10...0) (0...01 + 11 ... 1) (1...1! 2 apply Hadamards to the first n - 1 qubits, and then measure all n qubits in the {10),|1}} basis? Is this the same distribution or a different one than in part (a) and what did you expect? Show your work. C) (2 Points] What probability distribution over n-bit strings do we observe if we Hadamard all n qubits of the state from part (a), then measure all n qubits in the {10), 11)} basis? Show your work