Cryptography Reference
In-Depth Information
pulse from a laser (L) into a Mach-Zehnder interferometer via a circulator
(C). This interferometer splits the pulse into an advanced amplitude (P1) and
a retarded amplitude (P2). The amplitudes travel through phase modulators
(PM) on Bob's side and Alice's side, and are then attenuated (AT) to the single
photon level and reflected by Alice back to Bob. Although both P1 and P2 will
again be split at Bob's Mach-Zehnder interferometer, by gating his detector
appropriately, Bob can postselect those cases in which P1 takes the long path
and P2 takes the short path on the return trip. Thus the interfering amplitudes
experience identical delays on their round trip, ensuring insensitivity to drift
in Bob's interferometer.
The role of the phase modulators can be readily understood by examining
the space-time diagram of this protocol [see Figure 10.4(B)]. The eight boxes
(A1-A4, B1-B4) refer to the phase settings on the two modulators as the two
amplitudes pass through each of them twice. For example, B2 refers to the
phase acquired by the delayed amplitude of the pulse that Bob sends to Alice,
while B4 refers to the phase acquired by the same amplitude as it travels back
from Alice to Bob. It should be understood that B1-B4 refer to settings of the
same physical phase shifter at different times (and similarly for A1-A4). The
probability of a detection at Bob's detector is given by
P
d
∝
1
+
cos[
(
B2
−
B1
)
+
(
A2
−
A1
)
+
(
A4
−
A3
)
+
(
B4
−
B3
)
]
.
(10.4)
From this expression we see that only the relative phase between the phase
modulator settings affects the probability of detection. Thus, by setting
B1
A2, Alice and Bob can implement the interferometric ver-
sion of BB84 [14] by encoding their cryptographic key in the difference settings
φ
=
B2 and A1
=
≡
A4
−
A3 and
φ
≡
B4
−
B3. Since the resulting expression
A
B
P
d
∝
1
+
cos
(φ
A
+
φ
B
)
(10.5)
is independent of the time delay in Bob's interferometer and the absolute
phase settings in either modulator, Alice and Bob are able to achieve high-visi-
bility interference without initial calibration or active compensation of drift.
10.3.2 One-Way Noise-Immune Time-Bin-Coded
QKD
In this section, we describe a one-way noise-immune time-bin-coded QKD
scheme. The scheme also allows for Bob's apparatus to be passive. Before pre-
senting the full scheme, we review a non-noise-immune QKD scheme that mo-
tivates the technique used to combine noise-immunity and passive detection.
The two-photon quantum key distribution scheme described in Refer-
ence [8] has the remarkable property that both Alice and Bob use passive
detection (i.e., they are not required to switch between conjugate measure-
ment bases). In Reference [2], Gisin et al. suggest applying the AWI to generate
an associated one-photon scheme. We present a specific implementation of
this one-photon scheme here to show that it achieves passive detection by
enlarging the Hilbert space (see Figure 10.5). Let the advanced and delayed
