Cryptography Reference
In-Depth Information
delay 4
τ
) for the moment, we see that the second interferometer (with relative
delay
) enables the first two, or the last two, photons to meet at the second
beam splitter of this interferometer. If these two photons are in the singlet
state, they will leave by opposite ports. The contrapositive is also true: if they
leave by the same port (and are detected by one of the pairs of detectors on
each output port), then one can infer that they were not in the singlet state.
Returning to the first interferometer, we see that this interferometer provides
an opportunity for the first and last photons to be analyzed in a similar way.
Thus Bob's apparatus probabilistically chooses a pair out of the three photons
sent by Alice and determines whether the pair is in the singlet state or in some
orthogonal state [22]. Based on his detections, Bob can rule out at most one of
the three cases corresponding to Alice's possible signal states. Therefore, after
Bob has made his detection, Alice announces whether the run was a “data
run” (cases 1 or 2), or a “test run” (case 3). The data runs are used to share key
material, and the test runs are used to monitor the eavesdropper. The scheme
is noise-immune because the singlet state is immune to collective rotation.
τ
10.2.3 Symmetric Noise-Immune
Polarization-Coded QKD
We can apply the AWI one more time to get a six-photon symmetric scheme
[Figure 10.1(C)] from the three-photon one-way scheme by folding along the
dotted line in Figure 10.1(B). As indicated in Figure 10.1(C), this would yield
a six-photon entangled state. It is currently not practical to create such a state;
however, we can still implement the scheme using three pairs of entangled
photons in the state
| + 14 | + 25 | + 36 ,
(10.3)
| + =|
where
. The execution of the protocol is similar to the
one-way polarization protocol, except that instead of randomly choosing a
three-photon state and sending it to Bob, Alice uses the the apparatus depicted
in Figure 10.3 to choose randomly which pair of photons is in the singlet state.
For example, if Alice obtains a triple coincidence that indicates that photons
HH
+|
VV
Alice
Bob
τ
4
(same as Bob)
τ
S
123
654
Figure 10.3 A schematic of symmetric noise-immune polarization-coded QKD [see
Figure 10.1(C)]. A central source (S) emits three entangled pairs, so that Alice and Bob
each get one from each pair. The scheme works much the same as the one-way scheme
of Figure 10.2, except that Alice's apparatus makes a passive choice of the signal state
that Bob receives, as described in the text.
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