Cryptography Reference
In-Depth Information
in Reference [6], just as the preceding single-photon scheme follows from
the traditional phase-coding implementation. Let the states
in
Figure 10.6 be associated with the poles of the Poincare sphere. Instead of
using equatorial states and forcing Bob to postselect those cases for which
the advanced (delayed) amplitudes take the long (short) path, we use two
equatorial points (
|
1
and
|
2
) and the poles themselves to make up Alice's
four signal states. Signal states that are consistent with a given joint detection
are presented in the chart. As seen in Figure 10.5, each photon can lead to six
different detection events. Thus, since the new protocol involves two photons,
there are 36 possible detection events (see Figure 10.6).
The protocol operates as follows. As in BB84, Alice and Bob publicly
agree on an association of each of the four signal states (see Figure 10.6) with
logical values 0 or 1 (i.e., 1
|
3
and
|
4
1). For each run of the
experiment, Alice randomly chooses one of the four signal states and sends
it to Bob. When Bob detects both photons in their respective middle time
slots, he has effectively measured in the
→
0, 2
→
1, 3
→
0, 4
→
basis (the “phase” basis). When
Bob detects both photons in their early time slots, or both photons in their late
time slots, he has effectively measured in the
{
3
,
4
}
basis (the “time” basis) [25].
After the quantum transmission, Alice and Bob publicly announce their bases.
On the occasions when their bases match, Bob is able to infer the state that
Alice sent, based on his detection pattern using the chart in Figure 10.6. As
in single-qubit BB84, the occasions in which their bases do not match are
discarded. The scheme achieves passive detection (Bob is not required to make
any active changes to his apparatus) and noise-immunity (the phase delay in
Bob's interferometer does not affect any measured probabilities). The intrinsic
efficiency of the scheme is 1/4, compared to 1/2 for single-qubit BB84.
A proposed implementation for the source employed in Figure 10.6 is
presented in Figure 10.7. First, a pair of noncollinear, polarization-entangled
photons is produced via type-II spontaneous parametric down-conversion
from a nonlinear crystal pumped by a brief pulse [26]. Second, the modu-
lating element M performs one of four functions (filters one of the two po-
larization modes, or introduces one of two relative phases between the two
polarization modes), based on Alice's choice of signal states. Third, the two
{
1
,
2
}
P
+
SPDC
-
M
Source
Figure 10.7
A proposed implementation for the source employed in Figure 10.6.
SPDC is a nonlinear crystal pumped by a brief pulse to produce a noncollinear,
polarization-entangled two-photon state via spontaneous parametric down-conver-
sion. The action of elements M and P is described in the text.
