This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
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 i-X 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...
View Full Document
- Fall '08
- Computer Science