Cryptography Reference
In-Depth Information
in the quantum properties of two or more particles.
/
√
2
|
=
1
(
|
0
|
0
+|
1
|
1
)
(9.2)
1
2
1
2
is an example of a maximally entangled two-particle state. If one only looks
at one of the two particles, one finds it with equal probability in state
|
0> or in
state
1>. The state shows classical two-particle correlations in that when we
measure a 1 (0) in channel 1 this immediately implies a 1 (0) in channel 2. The
quantum state also shows strong correlation for any arbitrary superposition.
For instance, if we consider a polarization entangled state,
|
|
0> is
|
H> and
|
1>
is
V>. Measurements in any polarization direction in channel 1 will be 100%
correlated in channel 2.
|
9.3 Quantum Cryptography (Key Sharing)
Using the above coding, one could encode data on single photons, but com-
munication would be prone to errors due to loss; loss implies lost photons
and thus lost bits. More practical one photon per bit schemes revolve around
cryptographic key sharing where correlated random bit strings are generated
at separate locations. Only those photons that arrive are used to form the
key. Quantum key sharing has been demonstrated using faint pulses to ap-
proximate the one-photon superposition states [3-13] and using the strong
correlations inherent in the entangled state [17-22].
9.3.1 Faint Pulse Quantum Cryptography
9.3.1.1 The Method
We follow the first experimental realization [7], which is known as the BB84
protocol and was first described in [2]. In this protocol the transmitter (Alice)
encodes a random binary number in weak pulses of light using one linear po-
larization to encode 1's and orthogonally polarized pulses to encode 0's. To
prevent eavesdropping, the number of photons per pulse is limited to much
less than unity (the actual attenuation is linked to the overall transmission
and is usually chosen as 0.1 photons per pulse). Furthermore, the encoding
basis is randomly changed by introducing a 45
◦
polarization rotation on half
the sent pulses. In the receiver (Bob), single-photon-counting detectors detect
the pulses, converting the light to macroscopic electronic pulses. The two po-
larizations are separated in a polarizing beam splitter, and a 0 or 1 is recorded
depending on the detected polarization. A random switch selects whether to
measure on a 0
◦
or 45
◦
polarization basis. Owing to the initial weak pulse
and the subsequent attenuation along the transmission line, only very few
of the pulses sent result in detected photoevents at the receiver. A record
of when the pulses are detected is kept, and at the end of the transmission
the receiver uses a classical channel (e.g., a telephone line) to tell the sender
which pulses arrived and on what basis they were measured. All lost pulses
and all detected pulses measured on a different basis to the encoding basis
are erased from the sender's record. Thus identical random keys are retained
