Cryptography Reference
In-Depth Information
a)
b)
+/-
b3
b3
Pol
a1
PBS
b1
input
control bit
input
b1
output
a3
a1
a3
HWP
comp
Bell State
+
Φ
UV-pump
a2
comp
b4
a4
HWP 45°
a2
b2
input
b2
input
output
target bit
PBS
b4
Pol
b4
H/V
Figure 3.5 (a) The scheme to obtain a photonic realization of a CNOT gate with
two independent qubits. The qubits are encoded in the polarization of the photons.
The scheme makes use of linear optical components, polarization entanglement, and
postselection. When one and only one photon is detected at the polarization sensitive
detectors in the spatial modes b 3 and b 4 , the scheme works as a CNOT gate. (b) The
experimental setup. A type II spontaneous parametric down-conversion is used both
to produce the ancilla pair (in the spatial modes a 3 and a 4 ) and to produce the two input
qubits (in the spatial modes a 1 and a 2 ). In this case, initial entanglement polarization is
not desired, and it is destroyed by making the photons go through polarization filters,
which prepare the required input state. Half-wave plates (HWP) have been placed in
the photon paths in order to rotate the polarization; compensators (comp) are able to
nullify the birefringence effects of the nonlinear crystal. Overlap of the wavepackets
at the PBSs is assured through spatial and spectral filtering.
allow scalable quantum computation. This section will discuss the realization
of a CNOT gate, which operates on two polarization qubits carried by inde-
pendent photons and which satisfies the feed-forwardability criterion [41].
The scheme, shown in Figure 3.5, was first proposed by Franson et al. [42].
It performs a CNOT operation on the input photons in spatial modes a 1 and
a 2 ; the output qubits are contained in spatial modes b 1 and b 2 . The ancilla
photons in the spatial modes a 3 and a 4 are in the maximally entangled Bell
state
| φ +
1
=
2 ( |
H
|
H
+|
V
|
V
)
.
a 3 ,a 4
a 3
a 4
a 3
a 4
|
|
(a verti-
cally polarized photon) will denote our logical “0” and “1”. The CNOT opera-
tion for qubits encoded in polarization can be written as
In the following,
H
(a horizontally polarized photon) and
V
|
H
c |
H
t →|
H
c |
H
t ,
|
H
c |
V
t →|
H
c |
V
t ,
|
V
c |
H
t →|
V
c |
V
t ,
|
V
c |
V
t →|
V
c |
H
t , where the in-
dices c and t denote the control and target qubit.
The scheme works in those cases where one and only one photon is found
in each of the modes b 3 and b 4 . It combines two simpler gates, namely the
destructive CNOT and the quantum encoder. The first gate can be seen in
the lower part of Figure 3.5 and comprises a polarizing beam splitter (PBS2)
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