Page 87 - Principles and Applications of NanoMEMS Physics

74 Chapter 2

another particle which has never been anywhere near the first particle.” The
process does not involve sending any qubits, rather, the sender and the
receiver must have access to two other resources, namely, the ability to send
classical information, and an entangled EPR pairs of particles previously
shared between them.
As per the sketch of Figure 2-13, teleportation proceeds as follows.

1 1
ψ ψ
S S
e e
n n
d d R
2 2 e e e
r r c
e
i
EPR pair v ψ ψ
EPR pair
e
r
3 3

Figure 2-13. Quantum teleportation of state ψ . (After [108].)

There are three particles involved, namely, particle 1, whose unknown state
ψ = a 0 + b 1 (a and b are the unknowns) is to be teleported by a
1 1
sender to a receiver, and particles 2 and 3, which are prepared by an EPR
source into an entangled EPR state, for instance,

( 0 0 + 1 1 )
Φ + = 2 3 2 3 . (90)
23
2

Of these two entangled particles, one, namely, particle 3, is sent by the EPR
source to the receiver and the other, particle 2, is supplied to the sender.
Notice that locally both the sender and the receiver possess total knowledge
of the states of particles 2 and 3, respectively. However, globally, the three
states are described by tensor product state,

( 0 + ba 1 )( 0 0 + 1 1 )
ψ = 1 1 2 3 2 3 , (91)
123
2

consisting of the entangled pair, particles 2 and 3, and the unknown state.
Now, the specific actions that effect the teleportation are as follows. The