Problem 7. Consider the n-qubit GHZ state, |GHZ) and the n-qubit W state, (W), given by...

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Problem 7. Consider the n-qubit GHZ state, |GHZ) and the n-qubit W state, (W), given by |GHZ) = 1 |W) = 1 2 (10) n + 1) on), (|10...0) + |01...0). 0) + |01...0)... + 100...1)). Compute the reduced states (density matrices) of (a) Individual qubits (if the state is different for different qubits, specify), (b) Two qubits (if the state is different for different choices of two qubits, specify), (c) k qubits, where k n (if the state is different for different choices of the k qubits, specify). Problem 7. Consider the n-qubit GHZ state, |GHZ) and the n-qubit W state, (W), given by |GHZ) = 1 |W) = 1 2 (10) n + 1) on), (|10...0) + |01...0). 0) + |01...0)... + 100...1)). Compute the reduced states (density matrices) of (a) Individual qubits (if the state is different for different qubits, specify), (b) Two qubits (if the state is different for different choices of two qubits, specify), (c) k qubits, where k n (if the state is different for different choices of the k qubits, specify).