they are only 4 questions. Answer the one you can

a) b) The measurement postulate for quantum computation states that observable quantities are represented by hermitian operators. Show that hermitian operators have real eigenvalues and orthogonal eigenvectors. (5 Marks) A hermitian linear operator A acting on a 2 dimensional qubit space may be expressed as a 2x2 matrix. Explain how one establishes that such an operator is Hermitian. Verify whether or not the oy Pauli operator is Hermitian. Derive the eigenvalues and eigenvectors of the oy Pauli operator. (8 Marks) Using an example of your own show that a hermitian operator need not be unitary. Give an example of an operator that is normal, hermitian and unitary. c) (5 Marks) d) Show that a unitary operator is a normal operator. Is a Unitary operator always hermitian? Include examples to justify your claims (7 Marks) a) b) The measurement postulate for quantum computation states that observable quantities are represented by hermitian operators. Show that hermitian operators have real eigenvalues and orthogonal eigenvectors. (5 Marks) A hermitian linear operator A acting on a 2 dimensional qubit space may be expressed as a 2x2 matrix. Explain how one establishes that such an operator is Hermitian. Verify whether or not the oy Pauli operator is Hermitian. Derive the eigenvalues and eigenvectors of the oy Pauli operator. (8 Marks) Using an example of your own show that a hermitian operator need not be unitary. Give an example of an operator that is normal, hermitian and unitary. c) (5 Marks) d) Show that a unitary operator is a normal operator. Is a Unitary operator always hermitian? Include examples to justify your claims (7 Marks)