OVERVIEW OF QUANTUM COMPUTATION - Theoretical and Computational Research in the 21st Century - page 115

U ⊗ the one way to interlace two sys-
tems is allowing interaction between them.
Albert Einstein, Boris Podolsky and Nathan Rosen [14] were the fi rst
to note the consequences of existence of these two states; but when they
consider such a “no locality” nature as incomplete, they propose a local
hidden variable theory. Three decades later, John Bell [15-17] was able
to prove through schemes involving a local behavior of both subsystems.
Experiments obtained by Alan Aspect and his group [18-20] confi rmed
Quantum Theory predictions and established that natural behavior is “no
local.”

;

done by unitary operators like

A B

5.8 DECOHERENCE

Decoherence is the physical process in which the state that describes quan-
tum evolution of a system, loses its phase coherence [21, 22]. The physi-
cal origin of this process is the interaction between the considered system
and its environment (i.e., the external or internal degrees of freedom that
are not handy for spectator). That is why such an interaction causes that
system (S) and environment (A) variables correlates (separately) through
evolution, causing irreversible slack of interference effects of the quantum
system [21]. This happens even when the initial state of the system has
no correlations between both variables and it is a consequence of unitary
character of dynamic.

5.9 PHYSICAL IMPLEMENTATION: DIVINCENZO CRITERIA

At the moment of building any quantum algorithm that does a specific
task, a question arises: What physical resource is necessary to implement
this task in a real machine? The answer for this question was presented
by David DiVicenzo [23] in five criteria that must be carried out for any
propose of physical implementation of a quantum computer.
1. A physical system is scalable when qubits are well characterized.

2. It is necessary to have the ability to initialize the qubits in a basic

quantum state on a physical system.

3. Decoherence times of qubits must be much longer than the opera-

tion time of quantum gate.

4. If it is possible, set up a set of universal quantum gates.

5. If it is possible, have the aptitude to measure a specific qubit.