**Introduction
**

The Nobel Prize
of 2022 in Physics honours
initiatives to remove quantum strangeness from philosophical debates and put it
on experimental exhibit for all to observe. Alain Aspect
(France), John Clauser (USA), and Anton Zeilinger
(Austria), all shown a knowledge of entanglement, which
is a quantum link between
two particles that may exist across great distances, and they all received the Nobel
prize. Clauser and Aspect
conducted some of first "Bell tests" with entangled photons,
confirming quantum mechanics predictions and disproving several competing
theories which was based on classical
physics. Zeilinger demonstrated entanglement control strategies that can be
employed in quantum computing, quantum cryptography, and other quantum
information technologies using some of those Bell-test procedures.
Their
research findings cleared the path for future
quantum information-based technology.

Quantum mechanics has
already had incredible success since its conception in predicting the results
of tests. However, the theory assumes that aspects of a particle's properties
are intrinsically unpredictable, which alarmed many physicists, including
Albert Einstein. In 1935, he and his colleagues articulated a paradox in which
they stated their concern [1].

**Einstein- Podolsky-Rosen
(EPR)**

The
Gedanken-Experiment of Einstein- Podolsky-Rosen (EPR) was particularly
overlooked in terms of its significance in 1935. For approximately 30
years, it was completely ignored and thought to be useless [2].
"The EPR article was the single slip Einstein made!" Abraham
Pais had just released the blockbuster "Subtle is the Lord: The Science
and the Life of Albert Einstein" [3]. How terribly
inaccurate some predictions and judgements in the world of physics can be! When
John Bell had time to reflect about the Einstein-Podolsky-Rosen example in 1964
while on leave in the US, he prepared the paper "On the Einstein Podolsky-Rosen Paradox" [4], which included
Bell's inequality.

In general, Bell inequality is discrepancy
between the expectation values of two parties' joint measurements, Alice and
Bob in this instance. This discrepancy must be fulfilled by all local realistic
theories, but quantum physics deviates from this requirement. The Bell's Theorem is stated as "local realistic theories are
incompatible with quantum physics" and is based on Bell inequalities.
Bell's work did not spark any curiosity for an exceptionally long time.

Bell's
work demonstrated how to resolve the quantum versus classical viewpoint
conflict, but his suggested experiment made assumptions about detector
capabilities that were not realistic. In 1969, Clauser and his colleagues at
Columbia University proposed a redesigned version utilising photons and
polarizers [5]. That
experiment was successfully carried out three years later by Clauser and Stuart
Freedman, both of whom were affiliated with the University of California,
Berkeley [6].

**Bell's inequality tested**

In the Freedman-Clauser experiment, excited calcium atoms' entangled photons were utilised. Two different polarizers that were placed at specific orientations in relation to one another received the photons. Both photons passed through these polarizers at a rate that was consistent with predictions made by quantum physics.

Theoretically, Freedman
and Clauser demonstrated that when Alice and Bob's polarizers are offset from
one another by 22.5° or 67.5°, quantum mechanics predictions vary sharply from
hidden variable predictions. After gathering 200 hours of data, the researchers
discovered that the coincidence rates broke a revised version of Bell's
inequality, representing validity of quantum
mechanics (QM).

**John
Clauser **

John
Clauser did
postdoc from Columbia University, was the first to show interest in the topic
in the late 1960s. He was fascinated and motivated to provide support when he
read Bell's inequality work and discovered that it had a boundary for all unseen variable theories, which he accepted
as true. He decided to do the experiment as a result. The importance of these
kinds of experiments, nevertheless, was not understood at that time. Richard Feynman abruptly threw
Clauser out of his office when they met at Caltech to debate an EPR experimental configuration to test quantum mechanical
predictions, saying[7]: "Well, when
you have found an error in quantum-experimental theory's predictions, come back
then, and we can discuss your problem with it." Fortunately, Clauser didn't waver
and was committed to seeing the trial through. He sent letters to John Bell,
Louis de Broglie, and David Bohm, all of whom were regarded as realists, asking
for counsel or moral support. Let me quote Bell's response: [7]“In
view of the general success of quantum mechanics it is very hard for me to
doubt the outcome of such experiments. However,
I would prefer these experiments, to have been done. Moreover, there is always the slim
chance of an unexpected result, which would shake the world!”

Clauser,
a member of the 1960s' rebellious Hippie movement [8], undoubtedly
"wanted to shake the world", and in 1969 he submitted an abstract to
the American Physical Society's Spring Meeting recommending an experiment. After that, Abner Shimony invited him and revealed that he
and Michael Horne, one of his students, had very similar thoughts. As a result,
they came together and wrote the renowned CHSH paper [8] with Richard
Holt, a PhD candidate doing research with Francis Pipkin from Harvard. In this
publication, they presented an inequality that was well suited to experiments.
Along with Stuart Freedman, a doctoral student at Berkeley who earned his PhD degree for this experiment, Clauser eventually
carried out experiment in 1972.

A pair of photons released in atomic
radiative force
will be
appropriate for test of Bell inequality, as
stated in the CHSH study[8]. Clauser and
Freedman decided to use excited calcium atoms that were being pushed by lasers
since they were emitting the needed photon pairs. At the time, the signals were
so faint that a measurement would only endure for roughly 200 hours. A highly
useful inequality that Freedman derived was used for comparison with theory.
The experiment's conclusion is well recognized as they gained a pure breach of the Bell inequality that
was closely related to quantum mechanics. The consequence of subsequent trials
supported this conclusion. At
the time, conducting this experiment was a truly heroic feat because all the
necessary tools—including the laser—were homemade. Clauser was also only able
to work on the experiment because Charles H. Townes, who was interested in
Clauser's theories, gave him a job that would split his time between Clauser's
project and Townes' radio astronomy. Clauser was regrettably unable to pursue a
career in academia as a result of this experiment. But the fact that he has now
received the Nobel Prize can be considered as atonement.

**Alain
Aspect **

Young
French physicist Alain Aspect was so inspired by Bell's inequality article that
he chose to make it the focus of his thesis work. He went to see John Bell at
CERN to talk about his idea. Alain later informed that John's initial inquiry
to him was, "Do you have a permanent position?" Bell was terrified
that Aspect's career would be destroyed. The conversation couldn't start unless
Aspect responded in the positive to that question. Aspect wanted the setup to
have variable analysers. Early
in the 1980s, Aspect and his colleagues conducted a large number of tests [9], with the end
result being that each experiment dramatically violated the Bell inequalities
that were being employed.
Aspect's third experiment came near to addressing the locality gap, but it was
too difficult to conclude that it had due to the quasi-randomness of the
changing polarizers. Another loophole, known as the "detector-efficiency
loophole" or the "fair-sampling loophole," resulted from statistic
that, because we were unable to distinguish all photon pairs, a sample used in
the statistical calculations to make comparisons the results of the experiments
with Bell's inequalities could theoretically be biased. In fact, it was able to
replicate experimental findings deviating from local realist presumptions using
detectors from the early Bell's theorem experiments. The freedom of choice is
the name given to the third loophole. Now that the Nobel Prize
has been given out, this has been acknowledged.

**Anton
Zeilinger **

The
physics world first became aware of the significance and effects of such
Bell-type experiments in the 1990s, following Aspect's investigations. Bell
inequalities and quantum entanglement, at the centre of quantum theory,
communication, and computation, are attracting more and more attention.
Finally, there occurred a shift in public opinion on underlying principles of
quantum mechanics. At same time, technological advancements in electronics and
lasers were also being made. The development of recent source for producing two entangled
photons—specifically, impulsive
parametric down transfer—was
crucial. Here, a laser was used to pump a
nonlinear crystal, and pump photon split into two photons which travelled along two distinct cones.
The photons were horizontally polarised on one cone and vertically polarised on
the other. They became knotted in the area of overlap. Anton Zeilinger and his
team conducted their renowned tests using such an EPR source. Not only in
quantum physics and quantum information, but also in teaching and scientific
management, his efforts are significant and influential in a wide range of
fields. Zeilinger, also known as "Mr Beam," helped make science more
accessible to the general public. Zeilinger is the epitome of a Renaissance Academic
because of all of this as well as his love of philosophy and art.

Curiosity
has always been Zeilinger's primary motivation for studying physics. His
interest has always been centred in curiosity, even in experiments which have
made applications conceivable. Particularly noteworthy is the bravery he
displayed when, around 1990, he changed his field of expertise from neutron to
photon physics and accepted a position as a professor at University of
Innsbruck. There were obviously significant risks involved in this. But because
of his magnetic personality and uncanny sense of physics, Zeilinger attracted a
group of exceptionally gifted students around himself, with whom he conducted
fascinating experiments. Zeilinger
moved from Innsbruck to the University of Vienna in 1999 with his entire team,
where he was appointed Professor of Experimental Physics. His breakthrough was
the well-known experiment "Wave-particle duality of C60 molecules,"
which used large molecules like fullerenes to illustrate the effects of quantum
mechanical interference [10].
It paved the way for subsequent studies into interfering with much larger molecules,
under the direction of Markus Arndt.

Another
incredible quantum property was entanglement switching, which Anton and his
associates had already discovered in 1993. Actually, it is an entangled state
that was teleported. To put it more specifically, when two pairs of entangled
photons are measured for their Bell states, the other two photons in each pair
are instantly brought into the same entangled Bell state. In 1998, Zeilinger's
team experimentally implemented it [11].

Testing
Bell inequalities became increasingly popular in the late 1990s. At Geneva,
Nicolas Gisin's team used energy-time entangled photon pairs in photosensitive fibres to set a record.
They were successful in separating their spectators Alice and Bob by more
than 10 kilometres, and they were able to demonstrate that this distance had
almost no impact on the photons' ability to entangle. A vast array of
experiments exploring an
entanglement
of particles across long distances were conducted in new millennium by Bell inequalities. The main goal was to eventually be able to set
up world network in space [12].

**Experimental Results**

The
well-known
paper (EPR) by Einstein, Podolsky, and Rosen was published in 1935, and it
revealed the inadequacy of quantum theory. The scientists argued that if quantum
theory was
accurate, it would contradict common sense in the way that was revolting to a human mind that was more oriented towards
classical thought. Bohr's response was an confirmation of the reality that
quantum theory does exactly that rather than a denial of their reasoning.

They
were concerned with the theory's completeness and stated that "Every
aspect of the Physical Reality must have a counterpart in the Physical
Theory" is a requirement for a complete theory. They did not claim to be
capable of defining "Physical Reality," as it is used in this
context. Instead, they listed what they believed to be the very minimum
characteristics that a part of physical reality ought to possess. This
presumption, which seems so essential and clear, is what quantum theory
disproves. They suggested
that "there exists an element of physical reality corresponding to this
physical quantity if, without in any way altering a system, we can predict with
certainty (i.e., a probability equal to unity) the value of a physical
quantity." They provided one good example, but mostly discussion that
followed put different example provided by Bohm [2].

Consider a system having spin-0 that splits into two (½)
spin particles. The wave function would be such that particle 2 will have spin
down (↓) if particle 1 has spin up (↑), and vice versa. To maintain momentum, the two
particles will separate in different directions. If particle 1, which is
distant from decay point, has spin up, so it is certain that particle 2, which
is not here, has down spin. The down spin property must be a component of basic
reality, according to the EPR argument, as one hasn't interfered with particle
2 in any way. Being down spin is therefore a characteristic of the particle
itself and cannot have been caused by any measurement we took on particle 1. The
spin must be down when it left the decay point, the point of interaction.

Quantum
mechanics refutes this obvious point. It asserts that until the spin of 1^{st} particle is considered, the spin of 2^{nd} particle is unknown since
it is theoretically possible to experience interference between the possible
states because up until that point, it was in a superposition of up and down
states. This was the main topic of contention between Einstein and Bohr, although
it wasn't believed that the two points of view differed experimentally until
1965. Only then Bell demonstrate his theorem, which
states that if one conducts spin measurements in any direction, the assumption
that the spin is genuine severely limits the correlations that could
potentially exist between the particles. Since then, several investigations
have verified the findings of quantum theory [13].

It is intriguing that findings of Bell do not take account of
the scenario, which is directly addressed by the EPR argument, in which a
measurement of 1
particle permits one to predict with absolute confidence what would happen to another
particle. In this scenario, one particle's spin is measured, followed by
measurements of other particle either in same direction or in opposite direction. This instance not only
produce measurement certainty, but someone could
also attain
a classical system model that produces the same outcome. Quantum theory only
produces outcomes that differ from the classical ones in general scenario of a random angle between particles,
where one lacks certainty. For
example, using the wave function above, if particle 1's spin is measured in one
direction (n), while particle 2's spin is measured in different direction (l),
then expected value of
quantum mechanical correlation between two particles will be,

**E
(n · l) = ****〈****ψ|
(σ · n) (σ · l) |ψ****〉****
= -cos (n · l),**

and
this changes to cos (α – β) when particles are travelling in the ± z direction. On the other hand,
n and l are at angles α
and β and to the x-y plane. These cases—where the measurement orientations
diverge by 0° or 180°—provide examples of situations in which a firm forecast
is attainable. This situation, where an element of fact exists by means of
complete expectedness,
in accordance with EPR requirement, is known as the "super-classical"
case.

Bell
supposed
that spin of particles was determined at moment they divided in order to build a
model for association
in case of a deterministic and local theory. He gave an outcome a value of 1 because there
are only two potential values for the calculation of spin in a certain direction. Hence, he
provided a
value,

**Aλ
(n) · Bλ (l),**

Here both A and B may have values only l, which in this case
were controlled by some internal, hidden variable. He did this by measuring the
spin of both particles, one along n and the other along l. The product's main restriction was that, as
previously said, if l = n, one got

**Aλ
(n) · Bλ (n) = -1, **** ****Aλ
(n) · Bλ (-n) = +1.**

Finally, the measurement's expected value represented
the sum of all possibilities λ.

**E
(n, l) = ∫ dλ ρ(λ) Aλ (n) Bλ (****l****)**

He
could calculate the inequality,

**|E
(n, l) – E (n, k) | ≤ 1+ E (l, k)**

since
the probabilities are factorable (l, k). The quantum mechanical conclusion for
most angles eliminates this inequality. But regrettably, when l = ±n, it
provides zero information. One can create a straightforward predictable model
to describe the outcome in super-classical scenario, where one could create a certain statement but there, the Bell inequality above
provides no information. However,
the Bell inequality demonstrates that this is not feasible for general angles [13].

The
issue "Can one always discover a classical model for superclassical
case?" arises naturally as a result. From the perspective of Bell's
inequality, which is least fascinating case, but from the perspective of
reality, it is the most intriguing. In other words, Bell's theorem provides a
definitive response to the question of whether it is possible to create a
classical, localized, deterministic model that can replicate the general
conclusions of quantum theory. But it doesn't address whether one can create
such a model in the unique situation where precise predictions are possible, or
the EPR scenario. This
question also has a negative response. Yet, a more complex model than two-body
decay described above is required to provide an answer. We have created a
straightforward modification of the Bohm model that places more limitations on
the potential outcomes for different particles. So, the limit is so severe that even in
super-classical example, a deterministic, local model cannot be created, and
inequalities are not even necessary. One can demonstrate that it is impossible
to build such a model for any given value of hidden variable [14].

**Conclusion**

Recent
Bell inequality experiments had a considerable influence on how we
perceive reality. In contrast to "naive" realism, objects have
no qualities prior to observation, and the order of observations is not
important. Bell's Theorem also implies that nature is not local. All of these
"philosophical" experiments also resulted in very useful applications,
such as quantum information science, a growing area of study today.

Thus,
we arrive at the conclusion that even in easier case where one could make certain estimates in EPR sense, one cannot
do so with such a model. Furthermore, we also conclude that there is no way to
construct a classical, deterministic, local theory that replicates quantum theory in
general. To demonstrate this, one must move away from Bell theorem. Another final conclusion is that, with the proper
4-particle system, all that needs to be done to demonstrate that quantum theory
is valid experimentally is to show that it cannot be reproduced classically.
This means that it will be much simpler to refute the classical explanations
that are frequently offered to account for the outcomes of 2-particle
experiments that confirm quantum theory.

**Reference**s

[1] J.-W. Pan, D. Bouwmeester, M. Daniell,
H. Weinfurter, and A. Zeilinger, "Experimental test of quantum nonlocality
in three-photon Greenberger–Horne–Zeilinger entanglement," *Nature, *vol. 403, no. 6769, pp. 515-519,
2000.

[2] A. Einstein, B. Podolsky, and N.
Rosen, "Can quantum-mechanical description of physical reality be
considered complete?," *Physical
review, *vol. 47, no. 10, p. 777, 1935.

[3] A. Pais, "Subtle is the Lord…‘:
The Science and the Life of Albert Einstein. New York, NY: Oxford University
Press," 1982.

[4] J. S. Bell, "On the einstein
podolsky rosen paradox," *Physics
Physique Fizika, *vol. 1, no. 3, p. 195, 1964.

[5] J. F. Clauser, M. A. Horne, A.
Shimony, and R. A. Holt, "Proposed experiment to test local
hidden-variable theories," *Physical
review letters, *vol. 23, no. 15, p. 880, 1969.

[6] S. J. Freedman and J. F. Clauser,
"Experimental test of local hidden-variable theories," *Physical Review Letters, *vol. 28, no.
14, p. 938, 1972.

[7] R. A. Bertlmann, A. Zeilinger, and J.
F. Clauser, "Early History of Bell’s Theorem," *Quantum [Un] speakables: From Bell to Quantum Information, *pp.
61-98, 2002.

[8] J. F. Clauser, M. A. Horne, A.
Shimony, and R. A. Holt, "Proposed Experiment to Test Local Hidden
Variable Theories," *Physical Review
Letters, *vol. 24, no. 10, p. 549, 1970.

[9] A. Aspect, J. Dalibard, and G. Roger,
"Experimental test of Bell's inequalities using time-varying
analyzers," *Physical review letters,
*vol. 49, no. 25, p. 1804, 1982.

[10] M. Arndt, O. Nairz, J. Vos-Andreae, C.
Keller, G. Van der Zouw, and A. Zeilinger, "Wave–particle duality of C60
molecules," *nature, *vol. 401,
no. 6754, pp. 680-682, 1999.

[11] J.-W. Pan, D. Bouwmeester, H.
Weinfurter, and A. Zeilinger, "Experimental entanglement swapping:
entangling photons that never interacted," *Physical review letters, *vol. 80, no. 18, p. 3891, 1998.

[12] W. Tittel, J. Brendel, H. Zbinden, and
N. Gisin, "Violation of Bell inequalities by photons more than 10 km
apart," *Physical review letters, *vol.
81, no. 17, p. 3563, 1998.

[13] D. M. Greenberger, M. A. Horne, and A.
Zeilinger, "Going beyond Bell’s theorem," *Bell’s theorem, quantum theory and conceptions of the universe, *pp.
69-72, 1989.

[14] A. Drezet and B.
Stock, "A causal and continuous interpretation of the quantum theory:
About an original manuscript by David Bohm sent to Louis de Broglie in
1951," *arXiv preprint
arXiv:2103.00576, *2021.