Assignment2

# Assignment2 - February 2 2006 Physics 681-481 CS 483...

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February 2, 2006 Physics 681-481; CS 483: Assignment #2 (please hand in after the lecture, Thursday, February 16th) I. Non-spooky construction of a spooky 2-Qbit state Section A4 of the appendix to chapter 1 describes the strange properties of a pair of Qbits in the entangled state | Φ i given by: | Φ i = 1 12 ( 3 | 00 i + | 01 i + | 10 i - | 11 i ) . (1) To do this problem you do not have to read Section A4, which explains what is strange about the behavior of two Qbits in the state | Φ i . The problem is only about how to prepare two Qbits in that state — a prologue to A4.) It is easy to show (and you should convince yourself of this to make sure you understand the notation, but it is an example of the kind of routine algebraic manipulation that doesn’t have to be included in your essay) that | Φ i = ( H H ) | Ψ i , (2) where | Ψ i = 1 3 ( | 00 i + | 01 i + | 10 i ) , (3) so if you can produce a pair of Qbits in the state | Ψ i then you can get them into the state Φ by sending each through a Hadamard gate. This question is about how to get a pair of Qbits into the state | Ψ i , if they are initially in the standard state | 00 i (which is easily prepared with the aid of measurement gates and NOT gates, as described in chapter 1.) How would you go about changing the state of the

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