Cryptography Reference
In-Depth Information
Half-wave plates and nonlinear crystals in the paths provide the necessary
birefringence compensation, while the same half-wave plates are used to ad-
just the phase between the down-converted photons (i.e., to produce the state
φ
+
) and to implement the CNOT gate.
We then superpose the two photons at Alice's (Bob's) side in the modes
a
1
,a
3
(
at a polarizing beam splitter PBS1 (PBS2). The indistinguisha-
bility between the overlapping photons is improved by introducing narrow
bandwidth (3 nm) spectral filters at the outputs of the PBSs and monitor-
ing the outgoing photons by fiber-coupled detectors. The single-mode fiber
couplers guarantee good spatial overlap of the detected photons; the narrow
bandwidth filters stretch the coherence time to about 700 fs, substantially
larger than the pump pulse duration [44]. The temporal and spatial filtering
process effectively erases any possibility of distinguishing the photon pairs
and therefore allows two-photon quantum interference.
The described CNOT scheme is nondestructive, i.e., the output photons
can travel freely in space and may be further used in quantum communication
protocols. This is achieved by detecting one and only one photon in modes
b
3
and
b
4
. Since photon-number resolving detectors are not yet readily available
at this wavelength, we implement a fourfold coincidence detection to confirm
that photons actually arrive in the output modes
b
1
and
b
2
.
To demonstrate experimentally the working operation of the CNOT gate,
we first verify the CNOT truth table for input qubits in the computational basis
states
a
2
,a
4
)
. Figure 3.6(b) compares the count
rates for all 16 possible combinations. We then show that the gate also works
for a superposition of input states. The special case in which the control input
isa45
◦
polarized photon and the target qubit is an
|
H
|
H
,
|
H
|
V
,
|
V
|
H
, and
|
V
|
V
|
H
photon is particularly
interesting: we expect that the state
|+
a
1
|
H
a
2
evolves into the maximally
|
φ
+
b
1
,b
2
=
1
entangled state
a
2
as the input state; first we measure the count rates of the four combinations of
the output polarization (
√
2
(
|
H
b
1
|
H
b
2
+|
V
b
1
|
V
b
2
)
. We prepare
|+
a
1
|
H
|±
linear polarization basis an Ou-Hong-Mandel interference measurement is
possible; this is shown in Figure 3.6.
On the other hand, the same CNOT operation can be used to identify Bell
states when they are used as input states [45]. For this procedure, the gate
performs an operation that transforms each of the entangled Bell states into
well-defined but different separable states, which are simple to distinguish.
When a Bell state enters a CNOT gate in modes
a
1
and
a
2
, the gate operation
can be described by
|
H
|
H
,
...
,
|
V
|
V
) and then after going to the
|
φ
±
a
1
,a
2
→ |±
b
1
|
H
b
2
|
ψ
±
→ |±
|
V
b
2
.
a
1
,a
2
b
1
Figure 3.6 shows the count rates of all 16 possible combinations (four
different inputs and four different outputs). They clearly confirm the suc-
cessful implementation of the Bell state analyzer. The fidelity of each Bell
state analysis is
F
φ
+
=
(
0
.
75
±
0
.
05
)
,
F
φ
−
=
(
0
.
79
±
0
.
05
)
,
F
ψ
+
=
(
0
.
79
±
0
.
05
)
,
