Cryptography Reference
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mixed state, since any phase-flip error can be transformed to a bit-flip by
a rotation in a complementary basis. In these experiments, decoherence is
overcome to the extent that the technique would achieve tolerable error rates
for quantum repeaters in long-distance quantum communication based only
on linear optics and polarization entanglement.
Purification not only provides a way to implement long-distance quan-
tum communication but also plays an important role in fault-tolerant
quantum computation. Quantum error correction [32,33] allows a universal
quantum computer to be operated in a fault tolerant way [34,35]. However, in
order for quantum repeaters and quantum error correction schemes to work,
there are stringent requirements on the precision of logic operations between
two qubits. While the tolerable error rate of logic gates in quantum repeaters
is of the order of several percent [15], that in quantum error correction is of
the order of 10
−
4
to 10
−
5
, still far beyond experimental feasibility. Fortunately,
a recent study shows that entanglement purification can also be used to in-
crease the quality of logic operations between two qubits by several orders of
magnitude [36]. In essence, this implies that the threshold for tolerable error
in quantum computation is within reach using entanglement purification and
linear optics. Our experiments achieved an accuracy of local operations at the
PBS of about 98%, or equivalently an error probability of 2%. Together with
the high fidelity achieved in the latest photon teleportation experiments, the
present purification experiment implies that the threshold of tolerable error
rates in quantum repeaters can be well fulfilled. This opens the door to realistic
long-distance quantum communication. On the other hand, with the help of
entanglement purification the strict accuracy requirements of the gate opera-
tions for fault-tolerant quantum computation are also reachable, for example,
within the frame of linear optics quantum computation [37].
3.2.3 A Photonic Controlled NOT Gate
As can be seen above, advanced quantum communication protocols such
as entanglement purification may require nontrivial manipulation of qubits,
e.g., bilateral parity checks on pairs of photons (see Section 3.2.2). The under-
lying operations are typically elementary quantum gates, which are also used
for universal quantum computation. Well-known examples of such gates are
the controlled NOT (CNOT) and controlled phase (CPhase) operations. The
crucial trait of these gates is that they can change the entanglement between
qubits. A CNOT gate flips the value of the target bit if and only if the control
bit has the logical value 1 (see below). Entanglement can now be created be-
tween two independent input qubits if the control bit is in a superposition of
0 and 1. On the other hand, any Bell state that is fed into a CNOT gate will
result in distinct separable output states that make it possible to distinguish
all four Bell states deterministically.
In previous experiments [38,39,40] destructive linear optical gate oper-
ations have been realized. However, such schemes necessarily destroy the
output state and are hence not classically feed-forwardable, i.e., they do not
