Cryptography Reference
In-Depth Information
[25] of a free-space system over a relatively short distance outdoors in broad
daylight in 1996. The accidental detection rate due to the solar background
was minimized using a combination of narrow-band filters, short time win-
dows, and a small solid angle over which the signal was accepted. A number
of other groups [26,27] have now demonstrated similar systems over larger
ranges, and satellite systems of this kind are being considered. These systems
will probably have relatively high costs and small bandwidths.
The widespread use of quantum communications systems will require
both large bandwidth and operation over large distances. Although earlier
limitations due to polarization changes in fibers and the stability of inter-
ferometric implementations have now been overcome, it seems likely that
quantum repeaters [5,28,29] will be required in order to achieve the necessary
bandwidth and operational range. A promising approach for the implemen-
tation of a quantum repeater is described in the following sections.
6.3 Linear Optics Quantum Logic Gates
Quantum logic operations are inherently nonlinear, since one qubit must con-
trol the state of another qubit. In the case of photonic logic gates, this would
seem to require nonlinear optical effects, which are usually significant only
for high-intensity beams of light in nonlinear materials. As shown by Knill,
Laflamme, and Milburn (KLM), however, probabilistic quantum logic oper-
ations can be performed using linear optical elements, additional photons
(ancilla), and postselection based on the results of measurements made on
the ancilla [1].
The basic idea of linear optical logic gates is illustrated in Figure 6.2. Here
two qubits in the form of single photons form the input to the device and two
qubits emerge, having undergone the desired logical operation. In addition, a
number of ancilla photons also enter the device, where they are combined with
the two input qubits using linear optical elements, such as beamsplitters and
phase shifters. The quantum states of the ancilla are measured when they leave
the device, and there are three possible outcomes: (a) When certain outcomes
are obtained, the logic operation is known to have been correctly implemented
and the output of the device is accepted without change. (b) When other
measurement outcomes are obtained, the output of the device is incorrect,
but it can be corrected in a known way using a real-time correction known as
feedforward control, which we have recently demonstrated [30]. (c) For the
remaining measurement outcomes, the output is known to be incorrect and
cannot be corrected using feedforward control. The latter events are rejected
and are referred to as failure events. The probability of such a failure can scale
as 1/
n
or 1/
n
2
, depending on the approach that is used [1,2].
The original approach suggested by KLM was based on the use of nested
interferometers [1]. It was subsequently shown [6,31] that similar devices
could be implemented using polarization encoding, which had the advan-
tage of simplicity and lack of sensitivity to phase drifts. A controlled NOT
(CNOT) quantum logic gate implemented in this way [6] is shown in
