Information Technology Reference
In-Depth Information
1
2
(
)
If we choose every input register to remain in the
state, the
0
+
1
state of the set will be
(19)
which represents the tensor product of the
n
input states. Applying in Eq.
(19), the operator
ˆ
r
U
2
n
1
1
2
n
/2
x
f
(
x
) ,
(20)
x
=
0
And this state finally gathers all global properties of function
f
.
5.7 ENTANGLEMENT
Entanglement probably is the key, which defines the difference between
both quantum and classic theories of information; at the same time, this
property is the base for 2-qubits quantum gates. Considering a quantum
system made of two identical subsystems A and B, whose state spaces,
L
2
and
L
2
respectively, are considered two-dimensional and
f
, it is supposed
that bases of
L
2
and
L
2
are formed by kets
0
and
1
; the state space of set
system
{
}
.
Though not all states belonging to
L
1
2
have a understandable physical
interpretation; thus, while, for example, in
01
is plainly that A is in
0
and B is in
1
, in other cases such as superposition
1/2 00
2
2
2
will have as natural base the set
00 ,01,10 ,11
LLL
=
⊗
12
1
2
,
this is
harder to construe, although in this case, the state of A is
0
and B is a
0
and
1
superposition. Finally, we can consider other examples, where it
is not possible relate a quantum state to any of two subsystems indepen-
dently: such a circumstance appears, for example, in
(
)
+
10
(
)
ψ
1/
2
00
+
11 .
This last type of state, which is not possible to make a factorization with
the form
, is called Entanglement.
Such a state has the attribute of “no get information” if a “local” aver-
age is made in any of the subsystems: to be specifi c the result is entirely
random (the state is called completely mixed). The instantaneous conse-
quence of this is the impossibility to make these states through transformation
ψψ
⊗
A
B
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