February 2, 2006
Physics 681481; CS 483: Assignment #2
(please hand in after the lecture, Thursday, February 16th)
I. Nonspooky construction of a spooky 2Qbit 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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 Spring '08
 Ginsparg
 Conditional Probability, Qbits, 1Qbit unitary transformations

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