Information Technology Reference
In-Depth Information
This can be expanded to the following entangled form:
2
3
1
0
0
1
4
5
:
jψ >¼ η
(4.14)
[1 1]
0
, the top line. The
controlled NOT is controlled by the 1 component of the top line and causes a
NOT in the bottom line.
Entanglement could be interpreted to mean that the resultant
Note that the transform
H
, given below, creates
η
is not a
direct product of two qubits (without using addition somewhere). In contrast, a
non-entangled state vector can be factored into a product involving individual
qubits, for example, the following state vector is non-entangled since it can
be factored:
j
ψ >
2
4
3
5
¼
1
1
1
1
2
jψ >¼ η
H0
j
>
H0
j
>;
(4.15)
where
11
1
H
¼ η
(4.16)
1
0
[1 1]
0
and the reverse,
[1 1]
0
H
is a transformation that converts
0
>¼½
10
into
η
η
into [1 0]
0
. This reversible operation is assumed to be available physically.
If two entangled qubits are physically separated by a distance, while remaining
in a given quantum system, they would continue to be entangled. Say qubit
a
j
>
is
observed to be
0
j
>
. Then at a later time when qubit
b
j
>
is far removed, and when
observed, it will also be a
0
j
>
. Similarly if a
1
j
>
is read for
a
j
>
, then
b
j
>
has to
be a
1
. This feature is termed teleportation and theoretically occurs without
physical connections. For this to work, the qubits must not lose coherence because
of thermal agitation. It would be very exciting to discover someday that teleporta-
tion occurs within neurons causing hidden communications.
Simulated qubits, although potentially useful in a biological environment, can-
not achieve teleportation. A connecting interneuron is necessary. Simulated qubits
cannot achieve teleportation, but they can be synchronized, that is, they can be
made to start at the same time. And they can be made to be sampled at the same time
using a common sample pulse. This is suggested in Fig.
4.16
, showing that similar
frequencies give exactly the same sampled logic outputs. So in a sense, the state of
one simulated qubit determines the state of the other.
j
>
Search WWH ::
Custom Search