Cryptography Reference
In-Depth Information
Figure 2.2
The Poincare sphere representation of qubit states.
sphere, the so-called Poincare sphere (see Figure 2.2). Any couple of antipodal
points of this sphere corresponds to an orthonormal basis.
There are many physical systems whose degrees of freedom can imple-
ment a qubit. Quantum dots [10] or electronic levels of atoms in cavities QED
[11] are examples of such systems. For quantum communication, though, the
most natural candidate is provided by photons, because they are relatively
immune to decoherence when compared to other implementations, and be-
cause we generally do not need to make them interact much. Polarization is
often used to encode photonic qubits. Here we will describe an encoding that
is particularly well-suited for our purposes: the so-called time-bin qubits [6].
To prepare a time-bin qubit, one processes a short one-photon pulse at one
input port of an unbalanced interferometer [83] (see the left part of Figure 2.3).
One then gets a superposition of a state where one photon is in the lower arm
of the interferometer with a state where one photon is in the upper arm of
the interferometer. If the path length difference between the two arms chosen
is much larger than the spread of the pulse, it is possible to use a switch to
process on the same fiber the part of the pulse corresponding to the short path
and the part corresponding to the long path. Now
|
0
represents a one-photon
|
state localized in the late time-bin and
a one-photon state localized in the
early time-bin, as depicted in the middle of Figure 2.3. So, we see that by
tuning the phase and the coupling of the (left) interferometer, we can prepare
any (pure) qubit state.
As shown in the right part of Figure 2.3, we can use a similar interferome-
ter to perform measurements on a qubit. With the help of the switch, the first
time-bin is sent to the long arm and the second time-bin to the short one. The
path length difference between the two arms of this interferometer is chosen
to annihilate the time difference between the two time-bins, and make them
arrive simultaneously at the variable coupler. A photon is then detected by
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