Cryptography Reference
In-Depth Information
Alice
6
2
Source
Bob
+
+
τ
SW2
t
r
t
τ
τ
SW3
S
SW1
5
6
5
1
1
2
4
3
Figure 10.8 A schematic of symmetric noise-immune time-bin-coded QKD [see
Figure 10.1(F)]. A central source (S) emits two separately entangled photon pairs [see
Equation (10.6)]. One photon from each pair is sent to Bob. The other two photons
are sent through a series of three switches. The first switch (SW1) directs photon 1
along the lower path and photon 2 along the upper path. The action of the second
switch (SW2) is indicated by the labels t and r, which stand for transmit and reflect, re-
spectively. The third switch (SW3) directs photons 5 and 6 onto the same output fiber.
By postselecting the cases in which one photon is in position 5 and one photon is in
position 6, Alice effectively creates the four-photon entangled state in Equation (10.7).
This state is then analyzed by Alice and Bob with their Mach-Zehnder interferome-
ters, each of which has a delay equal to
τ
. The protocol used to establish a shared key
is described in the text.
four-photon entangled state
|
ELLE
+|
LEEL
.
(10.7)
5634
5634
short
path) in Alice's and Bob's Mach-Zehnder interferometers, Alice and Bob an-
nounce that they have measured in the phase basis, and they use the chart
in Figure 10.9 to infer the bit value. When one photon on each side does not
When all the amplitudes follow the pattern ( E
long path, L
Bob
Alice
Figure 10.9
Possible joint detection patterns for the scheme of Figure 10.8. The expres-
sion
detector
for the second. Given that the source produces the state in Equation (10.6), when all
the amplitudes follow the pattern ( E
( +
,
)
indicates that the
+
detector fired for the first photon and the
short) in Alice's and Bob's Mach-
Zehnder interferometers, the unchecked joint detection patterns do not occur because
of destructive interference. Thus Alice and Bob may use a publicly known encoding
(e.g.,
long, L
{ ( +
+ )
(
) }→
{ ( +
)
(
+ ) }→
,
,
,
0,
,
,
,
1) to agree on a secret key bit.
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