Cryptography Reference
In-Depth Information
Alice
Bob
+
+
+
a
L
E
c
b
Source
+
c
b
a
(
)
1
E
3
E
+
L
/
2
(
)
2
L
4
E
L
/
2
Time of Detection
±
±
±
a
b
c
{ }
{ }
{ }
+
2
,
3
4
1
2
,
4
1
3
,
4
Detector
{ }
{ }
{ }
2
,
3
4
1
2
,
3
1
3
,
4
Figure 10.5
A single-photon implementation of BB84 suggested in Reference [2]. The
kets
correspond respectively to an advanced (early) and a delayed (late)
single-photon wavepacket. Alice sends one of the four states listed below the diagram
of the apparatus. The chart indicates which of Alice's states are consistent with a given
measurement event at Bob's side. As described in the text, Bob's apparatus does not
require active change of measurement basis.
|
E
and
|
L
single-photon wavepackets be associated with the poles of the Poincare sphere.
The four states required for BB84 are typically taken from the equator, since a
single Mach-Zehnder interferometer can be used to generate any of the equa-
torial states. Instead, we imagine using two antipodal points on the equator
and the poles themselves. Bob analyzes the signal from Alice with a Mach-
Zehnder interferometer, recording which detector fired (one of two possibil-
ities) at which time (one of three possibilities). When Bob's detection is in
the first or third time positions, he can reliably distinguish between the pole
states based on the time of detection. When his detection is in the second time
position, he can reliably distinguish between the equatorial states based on
which detector fired. Thus Bob is no longer obliged to make an active change
to his apparatus to effect the requisite change of basis [23].
To see how this passive detection is derived from enlargement of the
Hilbert space, consider the quantum state of Alice's signal after Bob's
Mach-Zehnder interferometer. Alice's four states of one qubit are mapped
onto four mutually nonorthogonal states of a six-state quantum system (see
Figure 10.5). Thus by mapping a two-state quantum system into a six-state
quantum system, Bob is able to perform his part of the BB84 protocol with a
fixed-basis measurement in the six-state Hilbert space [24].
Next we present a scheme that combines passive detection with one-way
noise-immunity (see Figure 10.6). This scheme follows from that presented
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