Cryptography Reference
In-Depth Information
beams are combined with a relative temporal delay that matches the tem-
poral delay that Bob will subsequently introduce with his Mach-Zehnder
interferometer. This stage converts the photon pair from a pair of spatially
defined polarization-entangled qubits to a pair of polarization-defined time-
bin-entangled qubits. Finally, the element labeled P (for polarization) delays
and rotates one of the polarization modes by a duration much greater than
the delay of the third step, so that the delayed portion of the state is in the
same polarization mode as the nondelayed portion. Thus the two photons
sent from Alice to Bob have the wavepacket structure illustrated at the top of
Figure 10.6.
There are two noteworthy aspects of the configuration in Figure 10.7. First,
the technique introduced in Reference [8] for creating time-bin-entangled pho-
tons pairs only leads to superpositions of the correlated possibilities (i.e.,
|
EE
and
). The source presented in Figure 10.7 enables arbitrary superposi-
tions of the anticorrelated possibilities (i.e.,
|
LL
). Furthermore, the
correlated states can easily be created from this source by rotating the polariza-
tion axes at element M in Figure 10.7. In this way, all four time-bin-entangled
Bell states can be conveniently generated with this source. Second, the inter-
ference in Bob's interferometer results from the indistinguishability of photon
amplitudes that were initially in the same polarization mode. This is in con-
trast to configurations in which photon amplitudes from different polarization
modes are made indistinguishable by use of a polarization analyzer. Thus the
reduction in visibility that has come to be associated with extremely brief
pump pulses [15] will not be present in this scheme. Note that a symmetriza-
tion method has been developed to restore visibility for experiments using
polarization-entangled photons created by such a short pulse pump [16,17].
|
EL
and
|
LE
10.3.3 Symmetric Noise-Immune Time-Bin-Coded
QKD
In the symmetric time-bin scheme of Figure 10.1(F), the source produces a
four-photon entangled state. As it is currently not practical to create such a
state, we achieve the same result in Figure 10.8 by using two entangled pairs
in the state
(
|
EE
13
+|
LL
13
)(
|
EE
24
+|
LL
24
)
,
(10.6)
where
E
and
L
stand for early and late, respectively. The source apparatus
consists of three switches, while Alice and Bob simply have Mach-Zehnder
interferometers. The switches in the source behave as follows. 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, respectively. Thus for the early am-
plitude of photon 1 and the late amplitude of photon 2, SW2 reflects; other-
wise it transmits. The third switch (SW3) directs the photons 5 and 6 onto
the same output fiber. By postselecting only those occasions when one pho-
ton is found in the positions labeled 5 and 6, Alice effectively creates the
