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Unformatted text preview: 1 ¶ . Problem 3 (20 points) Consider an operator A in H 4 and four orthonormal eigenvectors:  ψ i i = α i 00 α i 01 α i 10 α i 11 1 ≤ i ≤ 4 . Construct the spectral decomposition of A . Problem 4 (20 points) Prove that the Hadamard operator on one qubit may be written as H = 1 √ 2 [(  i +  1 i ) h  +(  i  1 i ) h 1  ] Problem 5 (20 points) A quantum system is prepared in state  a i with probability 1 2 and in state  b i with probability 1 2 , where  a i = r 3 4  i + r 1 4  1 i and  b i = r 3 4  i r 1 4  1 i Calculate the corresponding density matrix ρ ....
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This note was uploaded on 08/08/2011 for the course COT 6600 taught by Professor Staff during the Fall '08 term at University of Central Florida.
 Fall '08
 Staff
 Computer Science

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