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sive processing of information that finally is traduced into an exponential
increase in calculus speed regarding classical devices.
5.3 UNITARY OPERATORS
Consider the behavior of static quantum systems, namely, systems that do
not change or evolve to another state with time, but do so when an external
factor strikes them. Its dynamic is described by the Schrödinger equation
and changes are because of external factors, expressed by lineal transfor-
mations or operators represented by a square matrix; these can be taken
state by state through a way that preserves the orthogonality of unitary op-
erators or unitary transformations [1], the only mathematical elements that
fulfill these requirements. For a set of
n
quantum systems of 2 states, the
operator acting on this is a matrix with dimension
22
n
n
. For example,
for a set of two quantum systems in which an operator acts,
×
⎛
⎞
⎛
⎞ ⎛
⎞
αβ
χη
aa
aa
+
αβ
χη
a
a
⎜
⎟
⎜
⎟ ⎜
⎟
=
0
1
(5)
0
⎜
⎟
⎜
⎟ ⎜⎟
+
⎝
⎠
⎝
⎠ ⎝⎠
1
0
1
(
)
U
αβ
χη
=
where
is the evolution operator, which is unitary. These
kinds of operators play an important role in the quantum computation area,
because of opening the possibility to create reversible information proce-
dure schemes.
5.4 QUANTUM MEASUREMENTS
Unlike measurements performed on macroscopic elements whose pro-
cesses give an absolute amount, in microscopic systems, the measurement
process of its states generates probabilities to find it in certain settings. As
soon as the measurement was performed, quantum mechanical predicts
that the system evolves to a different normalized state. To organize and
emphasize these ideas is necessary, remembering Eq. (4) with its natural
base
ψ
=
a
00
+
a
01
+
a
10
+
a
11 .
Suppose we want to mea-
00
01
10
11
ˆ
, this could only be possible
determining the probability to find the eigenvalue
a
n
of
A
associated to
this state, which is given by
sure the system in certain state
φ
m
n
=
A
ψ
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