Cryptography Reference
In-Depth Information
fidelity points for the
protocol as a function of the phase space dis-
tance,
r
, between the coherent amplitudes of the secret and reconstructed
states. The nonzero distance of
r
on the experimental points is due to mode
mismatch, optical losses, and imperfect phase locking. The corresponding
adversary structure obtained a fidelity of
{
1,2
}
F
{
3
}
=
0, since share
{
3
}
contains no
information about the secret state.
Similarly, Figure 8.9 shows an example of the secret and reconstructed
state for the
protocol. To allow for a direct measure of the overlap be-
tween the secret and reconstructed states, an inferred unitary squeezing oper-
ation was performed on the reconstructed state of this protocol. The inferred
Wigner function standard deviation contour after this unitary squeezing op-
eration is shown in the figure. Figure 8.10 shows the measured fidelity for
a range of gains. The amplitude quadrature gain, and subsequently
g
+
g
−
,
was controlled by varying the gain
G
of the photocurrent of the electro-optic
feedforward loop. At the unitary gain point, the best fidelity observed was
F
{
2
,
3
}
=
{
2,3
}
01 with corresponding optical quadrature gains of
g
+
g
−
=
0
.
63
±
0
.
(
1
.
77
±
0
.
01
)(
0
.
58
±
0
.
01
)
=
1
.
02
±
0
.
01 in this case. The corresponding adver-
sary structure
01.
The quantum nature of the (2,3) threshold quantum state sharing scheme
is demonstrated by the average fidelity over all the access structure permuta-
tions of
{
1
}
achieved an average fidelity of
F
{
1
}
=
0
.
03
±
0
.
F
=
.
±
.
F
clas
avg
=
/
3. This
can only be achieved using quantum resources and provides a direct verifi-
cation of the tripartite continuous variable entanglement between the shares
dealt to the players.
The quantum state sharing scheme was also characterized with the sig-
nal transfer (
0
74
0
04, which exceeds the classical limit
2
avg
) on, the reconstructed state.
The inset of Figure 8.11 shows the experimental
T
) to, and the additional noise (
V
T
and
V
points obtained
for the
protocol, plotted on orthogonal axes [23]. The theoretical point,
assuming no losses, is also shown. The
{
1,2
}
{
1,2
}
protocol achieved a best state re-
construction of
01. Both of these values
are close to optimal, being degraded only by optical losses and experimental
inefficiencies.
Figure 8.11 shows the experimental
T
{
1
,
2
}
=
1
.
77
±
0
.
05 and
V
{
1
,
2
}
=
0
.
01
±
0
.
}
protocol for a range of gains together with the theoretical curve for varying
electronic feedforward gain
G
. The adversary structure
T
and
V
points obtained for the
{
2,3
{
1
}
is also shown. The
accessible region for the
protocol without entanglement is illustrated by
the shaded region. The quantum nature of the state reconstruction is demon-
strated by the experimental points that exceed this classical region. For the
{
{
2,3
}
2,3
}
protocol the lowest reconstruction noise measured was
V
{
2
,
3
}
=
0
.
46
±
0
.
04 and the largest signal transfer was
T
{
2
,
3
}
=
1
.
03
±
0
.
03. The measured ex-
perimental points with
1 exceeded the information cloning limit [18],
demonstrating that for these points, the
T >
has better access to information
encoded on the secret state than any other parties. The adversary structure,
meanwhile, obtains significantly less information about the state reconstruc-
tion, with a mean signal transfer and reconstruction noise of
{
2,3
}
T
{
1
}
=
0
.
41
±
0
.
01
and
V
{
1
}
=
3
.
70
±
0
.
06, respectively. The separation of the adversary structure
