February 3, 2005
Physics 681481; CS 483: Assignment #2
(please hand in after the lecture, Thursday, February 17th)
I. Constructing a spooky 2qubit state
Section A3 of the appendix to chapter 1 describes the strange properties of a pair of
qubits in the entangled state

Φ
i
given by (1.129).
1
It follows from (1.131) that

Φ
i
=
(
H
⊗
H
)

Ψ
i
,
(1)
where

Ψ
i
=
1
√
3
(

00
i
+

01
i
+

10
i
)
,
(2)
so if you could produce a pair of qubits in the state

Ψ
i
you could easily get them into the
state Φ by sending each through a Hadamard gate. This question is about how to get a
pair of qubits 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 qubits from the easily prepared
and boring state

00
i
into the exotic state

Ψ
i
, if the gates that are available to you
are restricted by the following rules?
You are allowed to apply arbitrary 1qubit gates
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 Spring '05
 ANON
 Physics, Quantum computer, qubits

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