Quantum Entanglement Project

Awad, Falcone, Sharma, Tenhagen 1
Adam Awad, Mark Falcone, Shirshak Sharma, Andrew Tenhagen
Professor James O’Brien
PHYS 2500-01 Modern Physics
20 April 2016
Quantum Entanglement
Introduction
Quantum Entanglement is a phenomenon that scientists have been struggling with for
eighty years now. In understanding this concept, it is important to consider what is truly being
discussed. This is not just the complicated, confusing physics that people are used to being
confused by like quantum mechanics and wave functions. This is a concept that Einstein and
Schrodinger, among many of their other colleagues, struggled to fully understand and insisted
that the theory was “incomplete.” That being said, this idea of quantum entanglement can, on a
fundamental level be compared to the idea of twin telepathy. It gets referenced all the time in the
entertainment industry; the idea that twins have this natural connection that they have been
developing since birth. Due to this connection, twins are sometimes thought to have the same
thought at the same time, or to feel the same feeling as the other seemingly simultaneously. On
an entirely rudimentary level, this is a macroscopic example of what quantum entanglement
looks like.
Quantum Entanglement is a phenomenon in which pairs or groups of particles are made
or interact in a way that does not allow the particles to be described separately from one-another,
they must instead be described by a quantum state that represents the system as a whole. That
being said, physical measurements made on the entangled particles of position, momentum, spin,

etc. can all be found to be correlated. For example, if two particles are created in such a way that
their spin is known to be zero, then if the spin of one particle about a certain axis is known, then
the spin of the other particle about the same axis is known to be equal and opposite to the other
particle. That is, the spin of the two particles about a certain axis will be equal in magnitude and
opposite in direction.
History
The story of Quantum Entanglement begins in 1935 with Albert Einstein, in a joint paper
with Boris Podolsky and Nathan Rosen. In this paper, they formulated the EPR paradox
(Einstein, Podolsky, Rosen paradox), which attempted to explore the incomplete nature of
quantum mechanical theory. While they did not coin the name or even identify the strange
properties of this state, they were the ones to acknowledge that quantum mechanics was
incomplete, and they therefore began the conversation that led to the discovery of entanglement.
However, following the release of this paper, Erwin Schrodinger wrote a letter to Einstein in
which he used the word entanglement (the letter was written in German, but the translation was
given by Schrodinger himself) to “describe the correlations between two particles that interact
and then separate, as in the EPR experiment” (Kumar). Shortly thereafter, Schrödinger published
a paper defining and discussing the concept, and referring to it as entanglement. He recognized
the importance of the concept, and stated, “I would not call [entanglement] one but rather the
characteristic trait of quantum mechanics, the one that enforces its entire departure from classical
lines of thought” (Schrödinger). These scientists were all dissatisfied with the idea of
entanglement, because the transmission of information appeared to violate the universal speed
limit that was implicit in the theory of relativity. Einstein even went so far as to famously refer to

entanglement as “spooky action at a distance” (translated from the German, spukhafte
fernwirkung).
The EPR paper certainly generated interest in the physics community, and inspired
discussion about the foundations of quantum mechanics, but out of that came relatively little
published work. Despite the interest, the weak point in EPR’s argument was not discovered until
1964, when John Bell proved that the principle of locality, a key assumption in the EPR paper
which underlies the kind of hidden variables interpretation hoped for by EPR, was inconsistent
with the mathematical predictions of quantum theory. More specifically, he demonstrated an
upper limit, seen in Bell’s inequality, regarding the strength of correlations that can be produced
in any theory obeying local realism, and he showed that quantum theory predicts violations of his
limit for certain entangled systems. This inequality is experimentally testable, and there have
numerous experiments done to confirm it, starting with the work of Freedman and Clauser in
1972 and Aspect’s experiments in 1982. All of these experiments have confirmed quantum
mechanics, rather than agreeing with local realism. However, the issue still remained, because
each of these experiments had left open at least one loophole by which the validity of the results
could have been called into question. That is, until the Delft University of Technology performed
the world’s first loophole-free Bell test experiment in October 2015.
Concept
Entangled particles are particles which cannot be described as individual particles but
must be described in terms of the system as a whole. If particles are entangled, they cannot be
fully described without consideration for the other particles in the entangled system. Quantum
systems can become entangled in a variety of ways. One of the most common methods for the

entanglement of particles is referred to as spontaneous parametric down-conversion , which is
used to generate a pair of photons entangled in polarisation. Some other methods include the use
of a fiber coupler to confine and mix photons, the use of quantum dots to trap electrons until
decay occurs, and more. It is also possible to entangle quantum systems that never directly
interacted with one another. Similarly, entanglement can be broken when particles decohere
through interaction with the environment. One example of when particles decohere is when a
measurement is made.
The special properties of entanglement may be better understood and appreciated if the
two particles are separated. Imagine one particle being in Europe, and the other particle being in
the United States, and keep in mind this exercise is one purely of concept and understanding. If a
particular characteristic were measured on one of these particles, spin for example, and then
measure the same characteristic of the other particle, ensuring that it’s along the same axis, the
resultant measurements of the two particles will match, but in a complementary sense. That is to
say, if a particle of spin zero decays into two entangled particles, the spin of the two entangled
particles will be and , and will therefore sum to the original spin (maintaining the same axis− 2
1
2
1
of measurement).
Paradox
However, following the initial measurement mentioned previously the paradox of
entanglement comes into play. The paradox is that a measurement made on either particle will
collapse the state of the entangled system instantly, before any information about the
measurement could be communicated to the other particle. This is said with the assumption that
information cannot travel faster than light. In the quantum world, the spin measurement on one

particle is a collapse into a state in which each particle has definite spin in either (up or down)
direction along the axis about which they are measured. If the outcome is assumed to be random,
then each possibility has a probability of 50%. But if both spins are measured along the same
axis they are anti-correlated, which means that the random outcome made on one particle seems
to be transmitted to the other so that the other particle knows what it must be when it is also
measured. However, because of the timing and distance of the measurements, it is clear that for
this information to be exchanged at the rate that it does, it would be travelling faster than light.
According to special relativity though, this is impossible under any circumstances.
One possible resolution to this would be the hidden variables theory. This says that, from
the moment of separation, the state of the particle contains some hidden variables which
determine what the outcome of the spin measurements will be. This theory basically suggests
that each particle contains all the required information from the beginning, and that no
information is actually being transmitted at the time of the measurement. This was an early
theory which was originally believed by Einstein among others at the time to be the only way out
of the paradox, but it became clear over time that this theory fails when measurements of the spin
of entangled particles along different axes are considered.
If a large number of pairs of measurements of spin about different axes are made (on
different pairs of entangled particles), then the results should always satisfy Bell’s inequality,
according to local realism and the hidden variables theory. A number of experiments have shown
this to be false, all of which had loopholes until recently. The fundamental issue, however, about
measuring spin along different axes is that the measurements cannot have definite values at the

same time. This means they are incompatible because the maximum measurements’ precision is
constrained by the uncertainty principle.
Delft University of Technology Loophole-free Bell Test Experiment
Throughout the history of Bell test experiments, the results were frequently denied due to
the presence of loopholes such as the locality loophole which states that the observed entangled
particles and/or detectors are close enough that they can effectively communicate and react to
each other’s spin/results, or the detection loophole which states that the experiments may not
check all of the entangled pairs within the experiment thereby having an experiment based on a
non-representative selection. These loopholes were closed in the Delft University’s experiment
due to the fact that the entangled particles were 1.3 km away and the measurements of each
particle were taken far faster than even the speed of light could travel that distance thus closing
the locality loophole, as well as the fact that all of the entangled particles were measured, thereby
also closing the detection loophole. The experiment is rather fascinating and is succinctly
explained by the team at TU Delft in a video describing the experiment. Essentially two artificial
diamonds were placed 1.3 km apart on TU Delft’s campus, and within those two diamonds are
imperfections like all other diamonds. Within the many lattices of carbon that make up a
diamond, every now and then a nitrogen atom is present, and next to it, a carbon atom that is
missing. This is called a nitrogen vacancy, and where that missing carbon atom should be is an
electron trap. These electrons have spins, and, as is the point of the experiment, they have
“sisters”, i.e. electrons that they are entangled to within the other diamond 1.3 km away. In short,
the entangled electrons are excited with lasers, they emit photons that are entangled with the
electrons’ spins and they travel across campus until they meet, thereby entangling the electrons

and allowing for measurement of the electrons’ spins. This was done 245 times, resulting in a
correlation so strong that it disproves Einstein’s hidden variable theory. The experiment is
undeniably a huge success, having closed both loopholes simultaneously, as well as having been
the basis on which the Kavli Institute of Nanoscience reported that Quantum non-locality “is
supported at a 96% confidence level” (75).
Controversy
Even with the seeming conclusiveness of this experiment and all previous Bell test
experiments, convincing the scientific community that Einstein was--in one aspect--wrong, is no
easy feat. Is it not telling of the scientific community’s bias towards aligning with Einstein in
that the Laser Interferometer Gravitational-Wave Observatory’s (LIGO) discovery of
gravitational waves--a theory long-held by Einstein--was celebrated internationally when proven
to exist, but that an experiment (TU Delft’s loophole-free Bell test experiment) proving that
Einstein was wrong in one aspect seemingly fails to make a murmur?
This is hardly a surprise, as it does not take a physicist to tell you that Einstein is
regarded as a seemingly infallible prophet within the scientific community. Humorously enough,
when Bill Nye once answered a question regarding quantum entanglement, he prefaced his
answer with “if this turns out to be a real thing”, many, many years and experiments after it has
been repeatedly been proven to be, in fact, a real phenomenon.
Applications

Quantum Cryptography with Entangled Photons
Quantum cryptography exists both with and without entanglement. While entanglement
is not a necessary part of using quantum cryptography, it can greatly improve the existing
systems. If the same age-old example in which Alice and Bob are in separate locations trying to
communicate with one-another is used, then to use quantum cryptography without entanglement
would require some already shared knowledge between them. Basically, the quantum states can
be used to transmit a message from one person to the other so long as they share the same key. If
Alice sends a message to Bob using this without entanglement, then both participants must be
given the random key that would describe how to read this particular encrypted message. While
this can still be an improvement on current encryption methods, it still has significant security
weaknesses in the key distribution.
Using entangled particles opens up opportunity for potentially long distance, incredibly
secure, and faster than light communication. In addition, when using entangled photons on the
other hand, there is no need for the distribution of a key of any kind. Instead, it “comes into
existence at different locations simultaneously due to measurements on the individual members
of an entangled quantum system” [vcq]. If two qubits are being used, we can call them qubits 1
and 2. Then, to denote the two states of the qubit in a chosen basis, 0 and 1 can be used. State 1
represents a situation in which both qubits are in state 0 or in state 1. This means that
measurements on either qubit in that measurement basis results in 0 or 1, with the other qubit
exhibiting the same result due to the perfect correlation due to entanglement. Therefore, if
measurements were performed on many pairs, random sequences of 0 and 1 would be generated,
but because of the perfect correlations of entanglement, these measurements would be exactly

the same on both particles, and therefore the same results would be obtained by both Alice and
Bob, without any need for a key or cipher. Additionally, these perfect correlations hold for any
other basis that results from the original basis by a simple rotation so long as the phase factors
stay real. This trait can be exploited to exclude any eavesdroppers. This can be done by both
Alice and Bob switching around randomly from one base to another. This way, if they happen to
choose the same basis, they get perfect correlations and an eavesdropper is at a significant
disadvantage because he/she has a slim chance at properly guessing the basis chosen for a given
pair.
Quantum Computing
For quite some time now, entanglement has been viewed as a necessary part of quantum
computing. While there have recently been some propositions for quantum computing
possibilities without entanglement, it is still generally accepted that even if this were possible, it
would be less efficient than those computers that exploit entanglement. So whether or not
entanglement is a necessary part of quantum computing, it is certain that entanglement is a big
part of what makes the potential of quantum computing as efficient as it is.
Calculation
The Bell Experiment (simplified):
The original bell experiment set out to prove that Einstein's theory that the two particles
that were quantumly entangled had a “game plan” or that neither would actually be random. He
proposed that the particles had hidden information as to what they would measure for any
possible angle. The two possible outcomes for this theory would be:

For system 1: we get opposite spins 100% of the time. But the pairings for system 2 are as
follows
1 2 opposite?
(vertical)down (vertical) up yes
(vertical)down (right)down no
(vertical) down (left) down no
(right) up (vertical) up no

(right) up (right) down yes
(right) up (left) down yes
(left) up (verticle) up no
(left) up (right) down yes
(left) up (left) down yes
We get a total of 5/9 times that the particles are opposite. Now doing the standard calculations on
the system:
Say we measure the first particle using the vertical measurement and we get an up spin. Then
randomly pick a direction to measure particle 2. ⅔ of the time we will pick the wrong direction.
For both left and right since we know that the particle is going to be vertically down, we know
that it makes a 60 degree angle that we are measuring, the formula for the probability if
measured at a wrong angle is:
P(Downp2) = cos2
(θ/2)
Using a θ of 60 we get a Probability of ¾
Since ⅔ of the time we measure the right angle ¾ of the time. We get a total of ⅔ X ¾ = 2/4 or ½
Since we get the correct spin ½ of the time and not 5/9 of the time. We know for a fact that the
particles do not have a plan ahead of time; disproving Einstein’s hidden variable theory.

Future Research
Current information and theories on quantum entanglement leave much to be desired. A
great day of progress has been made, even in the last century in understanding entanglement, but
there is still a lot of work to be done. Much of the following research on entanglement will likely
be in isolating and eliminating any error or doubt in experiments, and figuring out exactly what
is going on that allows these strange interactions to happen.
However, aside from the concept of entanglement in general, research surrounding the
applications of entanglement will continue to be explored. People will continue to exploit
entanglement to master quantum cryptography, to create quantum computers, and hopefully even
find new applications for entanglement.
Conclusion
All in all, it is clear that Quantum Mechanics, and more specifically, Quantum
Entanglement, are just as confusing and controversial as ever. It is no surprise that this is the case
since many people incorrectly state that quantum entanglement breaks relativity thereby making
it false, when it does not, in fact, break relativity. However quantum entanglement does support,
if not outright prove, quantum non-locality, which breaks the law of locality or makes an
exception to it, rather. This is another reason why it still a contested topic despite overwhelming
evidence. With all of this in mind, one most definitely has to keep an open mind and be sure to
look at the research and evidence objectively, being careful to not bandwagon on Einstein’s
outdated theory that has been proven false simply because of his brilliance otherwise, while also
being careful to be thorough when reviewing new evidence.

References
http://www.tudelft.nl/en/current/latest-news/article/detail/einsteins-ongelijk-delfts-experiment-be
eindigt-80-jaar-oude-discussie/
https://www.youtube.com/watch?v=AE8MaQJkRcg
Kumar, M., Quantum, Icon Books, 2009, p. 313.
“Quantum Cryptography: Keeping Your Secrets Secret.” Phys.org. National University of
Singapore, 26 Mar. 2014. Web. 12 Apr. 2016.
Schrödinger E (1935). "Discussion of probability relations between separated
systems".Mathematical Proceedings of the Cambridge Philosophical Society 31 (4):
555–563.
"75 years of entanglement - Science News". Retrieved 10 April 2016.
Zeilinger, Anton. “Long-Distance Quantum Cryptography with Entangled Photons.”
Proceedings of SPIE(2007): n. pag. Web. 5 Apr. 2016

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