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Unformatted text preview: 1 + 2 along the same axis: R A ( 1 ) R A ( 1 ) = R A ( 1 + 2 ) Problem 3 (20 points) Show that the classical Fredkin and Tooli gates perform a fanout operation while their quantum counterparts do not violate the no cloning theorem. Hint: consider a control qubit in a superposition state 1 2 (  i +  1 i ). Problem 4 (30 points) Given a system with density operator and a set of orthonormal vectors  i i H n the spectral decomposition of the operator is: = X i i  i ih i  . The von Neumann entropy is S ( ) =tr( log ) =X i i log i . 1 Show that when = X i p i i then S ( ) =X i p i log p iX i p i S ( i ) or S ( ) = H ( p i )X i p i S ( i ) with H ( p i ) the Shannon entropy of a random variable X with the probability density function p X = p X ( x = i i ) = p i . 2...
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 Fall '08
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 Computer Science

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