Cryptography Reference
In-Depth Information
V
out
−|
δ
X
in
δ
X
out
|
V
out
.
V
cv
=
2
/
V
can be expressed in experimentally mea-
V
out
−
(
V
out
−
(
g
+
)
2
g
−
)
2
surable parameters as
.
Any one of the access structures can, in the ideal case, achieve perfect
state reconstruction corresponding to a signal transfer
V
=
(
)(
)
T
=
2 and additional
noise
V
=
0; the adversary structure obtains no information about the secret
state
T
=
0 and
V
=∞
.
8.5 Experimental Realization
8.5.1 Experimental Setup
Quantum state sharing has recently been experimentally demonstrated by
Lance et al. [25]. In this experiment, a Nd:YAG laser producing a coherent
laser field at 1064 nm was used to provide a shared time frame or
universal
local oscillator
among all parties. The secret quantum state was generated from
this laser field, by displacing the sideband frequency vacuum states of the
laser field using a phase and amplitude modulator.
The pair of quadrature entangled beams used in the dealer protocol
were generated from the interference of two amplitude squeezed beams. The
squeezed beams were produced using a pair of optical parametric amplifiers
(OPAs) seeded with 1064 nm light and pumped with 532 nm light, produced
from a second harmonic generator (SHG) [16]. A
2 phase shift was chosen
between the beams, which after interference on a 1:1 beam splitter exhibits
quadrature entanglement.
In order to enhance the security of the secret state against the adversaries,
the coherent quadrature amplitudes of the entangled beams were displaced
with Gaussian noise. Experimentally, this can be achieved by encoding broad-
band Gaussian noise onto the nonlinear crystals within the OPA resonators
at the sideband frequency of the secret state.
A homodyne detection system, consisting of a pair of balanced detectors
and the universal local oscillator with controllable optical phase, was used to
characterize the secret, adversary and reconstructed quantum states for the
reconstruction protocols.
π/
8.5.2 Experimental Results
Since the
reconstruction protocols are equivalent owing to the
symmetry of the player 1 and 2 shares, the (2,3) threshold quantum state
sharing scheme is demonstrated through the implementations of only the
{
{
1,3
}
and
{
2,3
}
reconstruction protocols.
Figure 8.8 shows the noise spectra for the secret and reconstructed state
for the
1,2
}
and
{
2,3
}
protocol. The corresponding inferred Wigner function standard
deviation contours were determined from these noise spectra and are shown
in Figure 8.8(c). For the
{
1,2
}
{
1,2
}
protocol, the best measured fidelity was
F
{
1
,
2
}
=
02 with corresponding optical quadrature gains of
g
+
=
0
.
93
±
0
.
0
.
94
±
0
.
01
and
g
−
=
0
.
97
±
0
.
01, respectively. Figure 8.8(d) shows several measured
