Cryptography Reference
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storage line
ψ
IN
ψ
PBS
OUT
Sagnac
switch
Figure 6.13 Polarizing Sagnac interferometer used as the switching element for a
single-photon memory device. A single photon can be stored in the delay line until
needed and then switched out again without changing its state of polarization, aside
from small technical errors. (Reprinted with permission from T.B. Pittman and J.D.
Franson, Phys. Rev. A, 66, 062302, 2002. Copyright 2002 by the American Physical
Society.)
As a result, it may be sufficient to consider a quantum repeater system
that compensates only for photon loss and simply ignores any other form of
error. Such a system can be implemented using a simple four-qubit encoding,
as shown by Dowling's group at the Jet Propulsion Laboratory (JPL) [5]. The
necessary encoding into four qubits can be done using the circuit shown in
Figure 6.14. It can be seen that this encoding can be accomplished using a
combination of CNOT logic gates and single-qubit operations, which can be
easily implemented in an optical approach.
Once the qubits have been encoded in this way, the effects of photon
loss can be corrected [5] using the circuit shown in Figure 6.15. Here a quan-
tum nondemolition measurement is designated by the abbreviation QND;
H represents an Hadamard transformation, the sigmas represent the usual
Pauli spin matrices and the polygons represent a single-photon source used
to replace any photons that have been lost. QND measurements can also be
implemented [29,36] using linear optical techniques, so that the entire error
correction process can be performed using the kinds of techniques that are
described above.
A quantum repeater would then consist of a series of error correction
circuits of this kind, separated by a sufficiently short distance L of optical
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