Cryptography Reference
In-Depth Information
useful for long distance communications. Therefore, one rather uses a source
that emits short pulses in a weak coherent state
|
φ
=|
φ
0
+|
φ
1
+|
φ
2
, where
|
φ
0
,
|
φ
1
,
|
φ
2
denote the zero-photon, one-photon and two-photon contribu-
tion to
respectively. If the source is weak enough, the two-photon contri-
bution can be neglected. Then, most of the time, no detector clicks. But if one
detector has clicked [84], the process which has occurred is exactly the one
that would have happened, had we had a genuine single-photon source. Our
second comment is about the use of optical switches. In practice, such de-
vices are quite lossy. Therefore, one can replace them with passive couplers.
There are then three possible arrival times for the photon, according to the
possible combinations of paths through the two interferometers. If eventu-
ally one photon is detected in the central time window, such variable couplers
behave as ideal optical switches. To summarize these two comments, we can
say that an ideal scheme can be replaced with a nonideal one at the price of
postselection. In addition, note that the detection of a photon in the left or
right satellite peak corresponds to a projection onto the early (
φ
)
time-bin, respectively. The use of a passive coupler in the analyzer does not
therefore engender additional losses, but guarantees a passive and random
selection of the measurement basis.
|
1
) or late (
|
0
2.3 Faint Laser Quantum Cryptography:
The Plug & Play Configuration
2.3.1 Basics of Faint Laser Quantum
Key Distribution
Quantum communication is about sending qubits from Alice to Bob. Quan-
tum cryptography (or better, quantum key distribution (QKD)) is about estab-
lishing a secret key (a string of random, secret bits) between Alice and Bob [7].
It exploits a fundamental principle of quantum mechanics, which is that one
cannot completely determine an unknown quantum state without disturbing
it [85]. The idea is that Alice and Bob can see whether the exchanged key has
been eavesdropped by checking to see if it has been disturbed. For this pur-
pose the qubits, in practice photons, must be sent and measured according
to a suitable protocol, the most widely known and applied being the BB84
protocol [18]. In this protocol, Alice sends, for example, photons with four dif-
ferent linear polarization states, of 0 or 90 and 45 or 135 degrees, respectively.
These are the four states indicated on the equator of the Poincare sphere of
Figure 2.2, the states on the poles representing right and left circularly po-
larized light, respectively (note that from the discussion held in the previ-
ous section, Alice could as well use time-bins; see the next section). Bob
cannot distinguish unambiguously between the four different states, how-
ever, he is measuring randomly along one of the two measurement bases
(0/90 or 45/145 degrees) and gets a conclusive result in half of the cases.
