Cryptography Reference
In-Depth Information
player 1
ψ
out
1:1
φ
player 2
Figure 8.5
Schematic of the reconstruction protocol for
{
1,2
}
.
ψ
out
: reconstructed
quantum state; 1:1: 50% reflectivity beamsplitter;
φ
phase delay.
8.4.2
Reconstruction Protocols
8.4.2.1
Reconstruction Protocol
As proposed by Tyc and Sanders, the access structure formed by players
1 and 2, henceforth denoted as
{
1,2
}
, reconstructs the secret quantum state
by completing a Mach-Zehnder interferometer, using a 1:1 beam splitter as
shown in Figure 8.5. The resulting output from the interferometer can be
expressed as
{
1,2
}
√
2
a
out
=
(
a
1
+
a
2
)/
=
a
in
(8.6)
Equation (8.6) clearly shows that the secret is perfectly reconstructed using
the
reconstruction protocol. In contrast, more complex protocols are
required for
{
1,2
}
{
2,3
}
or
{
1,3
}
to reconstruct the secret state.
Reconstruction Protocol
Using Two OPAs
As the access structures
8.4.2.2
{
2,3
}
and
{
1,3
}
{
2,3
}
and
{
1,3
}
are symmetric, we will only study the
{
reconstruction proto-
col follows an identical analysis. In the original proposal by Tyc and Sanders,
the
2,3
}
reconstruction protocol in the following. The
{
1,3
}
{
}
reconstruction protocols require two additional optical parametric
amplifiers, as shown in Figure 8.6. In this protocol, the access structure shares
from
2,3
are interfered on a 1:1 beam splitter. The two output fields are
then parametrically amplified and deamplified, respectively, using a pair of
optical amplifiers, each acting on one of the outputs. The optical parametric
amplifiers (OPAs) perform a unitary squeezing operation on the input fields,
squeezing one of the quadratures while antisqueezing the orthogonal quadra-
ture. The optical parametric amplifier acting on the first output squeezes
the amplitude quadrature, while the second optical parametric amplifier
squeezes the phase quadrature of the second output. The two beams are then
{
2,3
}
