Cryptography Reference
In-Depth Information
Each set consists of one hologram with charge
m
=
1 and another with charge
m
1. The first set of holograms provides the means of a transformation in
the three-dimensional space expanded by the states
=−
. The
second set, together with a single-mode fiber and a detector, acts as a projector
onto the three different basis states. All these elements are Bob's receiving de-
vice. Alice's photon also traverses a set of holograms, which, together with the
source and the detector on Alice's side, act as Alice's sending device. When-
ever Alice detects one photon, the transmission of a photon to Bob is initiated.
Due to the quantum correlations between the entangled photons, Alice can
radically control the state of the photon sent to Bob. In order to adjust their
respective devices properly, Bob has to perform a tomographic measurement
of the received state and classically to communicate his result to Alice.
In Figure 3.8 we present three examples of qutrits that were received by
Bob and remotely prepared by Alice. All of them were found to be very nearly
pure states, their largest eigenvalues and corresponding eigenvectors being
(a)
|−
1
,
|
0
, and
|
1
λ
=
0
.
99,
|
e
max
=
0
.
68
|
0
+
0
.
71
|
1
−
0
.
14
|−
1
; (b)
λ
=
0
.
99,
|
e
max
=
max
max
0
.
65
|
0
+
0
.
53 exp
(
−
i
0
.
26
π)
|
1
+
0
.
55 exp
(
−
i
0
.
6
π)
|−
1
; (c)
λ
=
0
.
99,
|
e
max
max
=
. From these exam-
ples it is shown that besides the relative intensities, Alice could also control the
relative phases of the states sent. Other reconstructed qutrits (not presented
in Figure 3.8) showed an effective suppression of the
0
.
58
|
0
+
0
.
58 exp
(
−
i
0
.
05
π)
|
1
+
0
.
58 exp
(
−
i
0
.
89
π)
|−
1
|
mode through de-
structive interference from the two holograms. The result was
0
λ
=
0
.
97,
max
|
. As can be de-
duced from the maximum eigenvalue of all the data, the purity of the recon-
structed states was larger than 97%. By direct comparison of the measured
data and the data estimated by the reconstructed matrix, the error was com-
parable to the statistical Poissonian noise, which demonstrates the reliability
of the tomography.
The method presented establishes a point-to-point communication pro-
tocol in a three-dimensional alphabet. Using the orbital angular momentum
of photons, we can implement the three basic tasks inherent in any communi-
cation or computing protocol: preparation, transmission, and reconstruction
of a qutrit. This communication scheme has already been experimentally im-
plemented in a quantum coin tossing experiment [64], which is an original
cryptographic protocol using qutrits.
e
max
=
0
.
26
|
0
+
0
.
68 exp
(
i
0
.
11
π)
|
1
+
0
.
68 exp
(
−
i
0
.
21
π)
|−
1
3.2.5 Entanglement-Based Quantum Cryptography
Quantum cryptography is the first technology in the area of quantum infor-
mation that is in the process of making the transition from purely fundamental
scientific research to an industrial application. In the last three years, several
companies have started developing quantum cryptography prototypes, and
the first products have hit the market. Up to now, these commercial products
were all based on various faint-pulse implementations of the BB84 proto-
col [5,65,66].
