Cryptography Reference
In-Depth Information
rewritten as
1
2
[
|
123
=|
1
|
−
23
=
−|
−
12
(α
|
H
3
+
β
|
V
3
)
−|
+
(α
|
3
−
β
|
3
)
H
V
(3.1)
12
+|
−
(α
|
V
3
+
β
|
H
3
)
12
+|
+
(α
|
V
3
−
β
|
H
3
)
]
.
12
It can thus be seen that a joint Bell measurement on photons 1 and 2
at Alice's side, i.e., a projection of particles 1 and 2 onto one of the four
Bell states, projects the state of photon 3 at Bob's side into one of the four
corresponding states, as shown in Equation (3.1). The outcome of the Bell
measurement is totally random (otherwise Alice and Bob could communicate
faster than light). However, when knowing Alice's measurement results, Bob
can perform a unitary transformation, independent of
|
χ
1
, on photon 3 and
convert its state into the initial state of photon 1.
3.2.1.1 Entanglement Swapping
An important feature of teleportation (also of relevance for long-
distance quantum communication) is that it provides no information whatso-
ever about the state being teleported. This means that an arbitrary unknown
quantum state can be teleported. In fact, the quantum state of a teleportee
particle does not have to be well defined, and it could thus even be entangled
with another photon. A Bell state measurement of two of the photons — one
each from two pairs of entangled photons — results in the remaining two
photons becoming entangled, even though they have never interacted in the
past (see Figure 3.1(a)). This was demonstrated recently by violating a Bell
inequality between particles that never interacted with each other [16] (see
Figure 3.1(b)). A chain of several entanglement swapping systems [17] can in
principle be used to transfer quantum entanglement between distant sites.
3.2.1.2 Scalable Teleportation
A recent result also of relevance for long-distance quantum communication
is the first realization of freely propagating teleported qubits [18], which will
eventually allow the subsequent use of teleported states. In previous experi-
mental realizations of teleportation with photons, the teleported qubit had to
be detected (and thus destroyed) to verify the success of the procedure. This
can be avoided by providing, on average, more entangled ancilla pairs than
states to be teleported. In the modified teleportation scheme (Figure 3.2), a
successful Bell state analysis results in freely propagating individual qubits,
which can be used for further cascaded teleportation. In many of our exper-
iments, two independent polarization entangled photon pairs, produced by
spontaneous parametric down-conversion (SPDC) with a probability
p
,are
used both for the preparation of the entangled pair
|
−
23
(photons 2 and 3)
and for the preparation of the initial state to be teleported (photons 1 and 4).
