# The Bridge - February 2018 - 30

Feature

Quantum
Teleportation:
from Sci-fi to
the Quantum Wi-fi

of quantum theory, it is possible to re-express the
combined systems |Ψ⟩S |Φ⟩AB (1) as
(1)

by: Daniel Cavalcanti and Paul Skrzypczyk

Travelling from one place to another without having
to make the journey along the way is a science
ﬁction dream immortalised in the famus Startrek's
quote "Beam me up, Scotty!" [1]. In 1993 a group of
six bright scientists showed that the rules of quantum
physics allow for a very similar phenomenon,
which they named quantum teleportation [2]. Their
seminal paper quickly became recognised as a
breakthrough in physics (it is the most cited paper
in the ﬁeld of quantum information). In the past 20
years, quantum teleportation has been implemented
in a variety of physical setups, over distances of up
to 1,400 kilometres, from a ground laboratory to a
satellite [3].
Quantum teleportation is the process in which an
unknown quantum state of a system S, held by a
party customarily called Alice, is transferred to a
system B, held by a party called Bob, who is in a
far away location. In order to accomplish this task,
Alice and Bob must share a pair of systems which
are in a very special quantum state - known as
a maximally entangled state (which serves as the
physical 'channel' through which teleportation takes
place) and Alice must communicate a small amount
of additional classical information to Bob.
Mathematically, quantum teleportation can actually
be easily understood, relying only on basic aspects
of quantum theory. Suppose Alice has been given a
system S in a generic quantum state Ψ⟩S= a |0⟩ + b
|1⟩. Moreover, her and Bob share a bipartite system
AB in a maximally entangled state |Φ⟩AB = (|00⟩ +
|11⟩)/√ 2. Using the famous superposition principle
THE BRIDGE

What this mathematical identity shows is that
if Alice applies a measurement on her systems
S and A corresponding to the projections onto
the states (|00⟩+|11⟩)/√2, (|00⟩−|11⟩)/ √2,
(|01⟩+|10⟩)/√ 2, and (|01⟩−|10⟩)/√ 2 (this special
measurement is called a Bell state measurement)
Bob is automatically left with one of the four states
a 0⟩ + b |1⟩ , a |0⟩ − b |1⟩ , b |0⟩ + a |1⟩ or b |0⟩
− a |1⟩ Notice that the first state is in fact already
the original state |Ψ⟩ that Alice wants to teleport
to Bob, while the other three can be transformed
into |Ψ⟩ by appropriate transformations (|1⟩ →
− |1⟩ , |0⟩ ↔ |1⟩, or both). In other words, Alice
applies a measurement to her systems S and A,
and, conditioned to the outcome she observes the
system of Bob will acquire a state that is the same as
the original state of S after an appropriate correction.
Bob doesn't know which correction, if any, to make
until he learns the result of Alice's measurement,
which is exactly what she must communicate to him.
There are a number of important aspects worth
noting about quantum teleportation. First, unlike
the sci-fi idea of disappearing here and appearing
there, in quantum teleportation it is not the physical
system that is transferred from one place to another,
but only its state. This is actually very interesting,
because systems S and B can actually be completely
different types of physical systems! For example
photons and atoms [4]. Second, due to the classical

Contents
The Bridge - February 2018 - Cover1
The Bridge - February 2018 - Cover2
The Bridge - February 2018 - Contents
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