The EPR paradox describes two entangled particles in uncertain states until measured, at which point their states become certain and correlated, suggesting faster-than-light communication. Quantum information science uses properties of superposition and entanglement, like in EPR pairs, for applications such as quantum teleportation, super-dense coding, and quantum key distribution. Quantum teleportation uses EPR pairs and measurements to transmit a qubit's state from one place to another. Super-dense coding exploits entanglement to transmit two classical bits using one qubit. Quantum key distribution uses EPR pairs to securely exchange encryption keys.

1. School of Science and Technology
EPR Paradox
Defining the EPR Paradox
The EPR paradox is one of the best known examples of quantum
entanglement. It involves two particles in an entangled state where each
particle is in an uncertain state until measured, at which point the state
becomes certain and the same is true for the other particle. The reason
that EPR is still classed as a paradox today is because it suggests
instantaneous communication between the two particles at speeds greater
than light, conflicting with Einstein’s theory of relativity. From this, we can
say an EPR pair is a pair of qubits which are entangled, also known as Bell
states, where the following four states are that of a 2-qubit system.
Origins
In the 1930s Einstein along with his colleagues Podolsky and Rosen
developed the EPR paradox as a way of showing that the theory was
inconsistent with other laws of physics. Later, in 1951, Bohm modified and
reformulated the paradox. Both stated that an unstable particle with spin 0
decayed into two particles, A and B both moving in opposite directions. As
the initial particle had spin 0, the sum of the two new particles also
needed to equal 0 (obeying the conservation of energy law). For example,
if particle A had a spin of -1/2 then particle B would have spin +1/2.
Furthermore, until measured, neither particle had a defined state but
instead were in superposition’s of the two states with equal probability of
having a positive or negative spin.
Aim
Do we have the capability to extend our theory of communication? Is it
possible to improve the way in which we encrypt our information? Well an
answer may come in the not so distant future. Quantum theory has
developed a good deal since the early 20th century and looks to provide
viable answers to some of the questions posed above. With companies
such as IBM and D-Wave Systems investing so many resources into
research within quantum computing, it is easy to see how such advances
in quantum science will minimise current issues we face today when
considering the scope of ever-emerging technology. My aim is to provide
an introduction into some aspects of quantum information science, namely
the applications of EPR pairs.
Introduction
Quantum Information Science (QIS) combines aspects of
Mathematics, Physics, Computer Science and Information Theory with
potential advances in the field of computation, communication and
fundamental quantum science. When considering the applications of the
encoding of information in quantum states, we are interested in the
properties of superposition and entanglement. These are two fundamental
quantum characteristics, the first of which is arguably the basis of
quantum computing when compared to classical computers. Superposition
describes a qubit in a linear combination of the basis states |0> and |1>
whereas entanglement describes a pair of particles that can only be
described as one in a given quantum state system. These two definitions
provide the building blocks for understanding EPR pairs and their
applications to quantum information science.
Quantum Teleportation
Quantum teleportation arises from the phenomena of quantum
entanglement and describes a way in which quantum information can be
transmitted from one place to another. In order to perform quantum
teleportation of a qubit, Alice and Bob need to first produce two entangled
qubits in one of the 4 bell states. A circuit representing quantum
teleportation is shown below.
In the circuit above the upper two qubits belong to Alice whilst the bottom
qubit belongs to Bob. In order to transmit the entangled information to
Bob, the qubits must pass through a number of quantum gates as shown in
the diagram. The result of the measurement, denoted M, feeds into some
circuit that Bob uses to transform his qubit in the correct way. The state of
Bob’s qubit is now identical to the state Alice aimed to transmit. However it
should be mentioned that this is not a copy, Alice’s qubit is completely
destroyed when she makes the measurement. Various experiments
showing quantum teleportation have been conducted using photons,
however, in recent work, more complex quantum states for example whole
atoms of Beryllium have been teleported in laboratories.
Super-Dense Coding
Super-dense coding can often be described as somewhat the opposite of
quantum teleportation, in the fact that it uses one qubit to send two
classical bits, rather than two classical bits to send one qubit. In general, it
is impossible to extract more than one classical bit of information from a
single qubit. However, if Alice receives a two-bit classical message and then
transmits that message by performing a unitary transformations (as shown
below) on a entangled pair of qubits (EPR pair), she can share this with Bob
and consequently send that qubit to Bob. Therefore showing how one qubit
can carry two classical bits of information. A depiction of how this works is
shown in the circuit below.
Quantum Key Distribution
One of the most interesting and exciting applications of EPR pairs is
quantum key distribution (QKD). Unlike other applications of quantum
information science, QKD is practical with current technology and can be
demonstrated via optic fibre and ground-to-satellite optical links. QKD uses
quantum properties to exchange secret information which can then be used
to encrypt messages that are communicated over an insecure channel. It
works because eavesdropping or measuring the quantum system disturbs
the system, which effectively leaves detectible traces of interference. Alice
and Bob, the parties exchanging information, can then decide either reduce
the information over the channel or discard the corrupted information
completely. Examples of QKD include the BB84 protocol and the E91
protocol which both encode quantum information in discrete variables.
References
• Jones, Z. (October 2015). EPR Paradox. Available:
http://physics.about.com/od/physicsetoh/g/EPRparadox.html. Last accessed 19th Aug 2016.
• Kaye, P (2007). An Introduction to Quantum Computing. New York: Oxford University Press.
p78-85.
• Preskill, J. (1999). Quantum Information Science. Available:
http://www.nsf.gov/pubs/2000/nsf00101/nsf00101.htm. Last accessed 21st Aug 2016.
EPR pairs and their applications
in Quantum Information Science
Arandeep Singh Kaila