Which of the following statements is (are) true for the CNOT gate?
A. CNOT can be used to generate entangled state from a pair of separable states.
B. CNOT is hermitian.
C. CNOT gate is its own inverse.
D. CNOT is unitary
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CNOT Properties Clarified.
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Which of the following statements is (are) true for the CNOT gate?
A. CNOT can be used to generate entangled state from a pair of separable states.
B. CNOT is hermitian.
C. CNOT gate is its own inverse.
D. CNOT is unitary
A, B , D
A. CNOT can be used to generate an entangled state from a pair of separable states.
This statement is true. The CNOT gate, also known as the controlled-NOT gate, is commonly used to generate entangled states. By applying the CNOT gate to a pair of qubits in the |0⟩ state and |+⟩ state, for example, it can create an entangled Bell state.
C. CNOT gate is its own inverse.
This statement is true. The CNOT gate is its own inverse, meaning that applying the CNOT gate twice will result in the original state. If the target qubit is initially in the |0⟩ state, applying the CNOT gate twice will return the control and target qubits to their original states.
D. CNOT is unitary.
This statement is true. The CNOT gate is a unitary gate, which means it preserves the normalization of quantum states and is reversible. Unitary gates are important in quantum computing as they ensure that quantum computations are reversible and do not lose information.
B. CNOT is Hermitian.
This statement is false. The CNOT gate is not Hermitian. A Hermitian operator is one that is equal to its own conjugate transpose. While the CNOT gate is its own inverse, it does not satisfy the additional requirement of being Hermitian.
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