Cryptography Reference
In-Depth Information
player 1
{1,3} and {2,3}
ψ
out
g
OPA
player 2
pump
1:1
1:1
1/
g
φ
φ
OPA
player 3
Figure 8.6
Schematic of the 2 OPA reconstruction protocol for
{
2,3
}
and
{
1,3
}
. OPA(g):
optical parametric amplifier with parametric gain g;
ψ
out
: reconstructed quantum
state; 1:1: 50% reflectivity beam splitter;
φ
phase delay.
interfered on another 1:1 beamsplitter. The resulting output beam can then be
expressed as
X
in
√
g
√
2
α
±
δ
X
sqz1
+
δN
+
1
2
√
2
1
√
g
1
X
out
=
δ
δ
+
+
X
sqz2
+
δN
−
√
2
β
±
δ
1
+
(8.7)
where
g
is the gain of the of
p
tica
l p
ara
m
etric am
p
lifiers, and the param
e
ters
a
re
d
efi
ned as
∓
√
2
±
√
2
±
√
2
)/
√
g
+
√
g
)/
√
g
α
±
=
(
−
β
±
=
(
−
1
(
−
1
)
and
1
+
√
2). By choosing a correct gain for the optical parametric
a
mpl
ifi
ers,
it is possible to reconstruct the secret state. Setting the gain to
√
g
√
g
(
−
1
∓
=
√
2
+
1,
the quadratures of the reconstructed secret simplify to
√
2
X
out
=
δ
X
ψ
−
X
sqz2
δ
δ
(8.8)
√
2
X
out
=
δ
X
ψ
−
X
sqz1
δ
δ
(8.9)
Equation (8.8) shows that in the ideal limit of perfect squeezing and with
correct gain for the optical parametric amplifiers, the access structure can
perfectly reconstruct the secret state.
The Tyc and Sanders [14] original scheme requires significant resources
including a pair of entangled beams and two optical parametric amplifiers.
Furthermore, the reconstruction protocol requires that the gain of the phase-
sensitive amplifiers be controlled precisely and that they have a high nonlin-
earity. Each of these requirements is difficult to achieve experimentally. High
nonlinearity can be achieved either in Q-switched or mode-locked setups,
or by enhancing the optical intensities within optical resonators. These tech-
niques, however, result in losses and reduced quantum efficiency. For these
