Quantum bounds are numbers (such as 4, 6, and 2√2) that naturally appear in quantum experiments, similar to how the number π emerges in circles. But just as how π pops up in a wide variety of areas beyond circles, in a new study physicists have found that quantum bounds are not exclusive to quantum theory but also emerge in purely classical experiments. The results suggest that attempts to define quantumness should not be concerned with quantum bounds, since there is nothing inherently quantum about them.

The physicists, Diego Frustaglia

*et al*., at the University of Sevilla in Spain, have published a paper on the emergence of quantum bounds in classical experiments in a recent issue of

*Physical Review Letters*.

**Different experiments, same bounds**

In their study, the researchers
performed three classical experiments that correspond to three famous quantum
experiments involving quantum bounds. These quantum experiments are a
sequential version of the Bell inequality and two other related quantum inequalities,
all of which are used to distinguish between quantum and classical phenomena.

In order to show that a system
exhibits quantum effects, these experiments traditionally attempt to show that
a system can violate a quantum inequality. The greater the violation, the more
quantum the system. The maximum violation of a quantum inequality is the
quantum bound. The quantum bounds arise from probability distributions in the
experiments and are specific numbers—for instance, the Bell inequality has a
quantum bound of 2√2 (approximately 2.82), which is known as Tsirelson's bound.
The other two inequalities addressed here have quantum bounds of 4 and 6. Both
theoretically and experimentally, no violation of a quantum inequality has ever
surpassed these bounds.

In the new study, the researchers
showed that these same quantum bounds emerge in experiments in which classical
waves travel along an ordinary transmission line. The researchers found that
the probabilities originating from the detection of wave intensities at the end
of the transmission line follow the same distribution as the probabilities of
detecting violations of the quantum inequalities. Specifically, the classical
experiments yield bounds of 2.78, 3.93, and 5.93 for the three analogous
experiments. In all three cases, these values are actually slightly closer to
their theoretical values mentioned above than the values obtained in quantum
experiments are, providing strong evidence that both quantum and classical
experiments produce the same bounds.

**Interpreting the results**

One of the many implications of the
study is that it offers new insight into what it means to be quantum. By
showing that quantum bounds are not unique to quantum theory, but are universal
bounds, the findings show that ongoing attempts to define quantum theory should
not focus on these bounds.

Instead, the results provide a clue
for finding a true quantum feature by revealing an important difference between
the way in which the classical and quantum
systems produce the same bounds. While the classical
systems require some kind of extra resource, such as memory, the
quantum systems do not. So a complete description of quantum theory should
explain how quantum systems can violate the same bounds that classical systems
do, but without using extra resources.

As the researchers explain, this
approach of investigating classical systems to better understand quantum
mechanics tends to be the opposite of most research.

"We somehow reverted the
strategy followed by the founders of quantum theory," Frustaglia told

*Phys.org*. "In the early times of quantum mechanics, microscopic systems were subject to an intense questioning naturally biased towards classical physics. The result was a set of oddities interpreted as the paradigmatic features of the quantum realm: the particle-wave duality (is it a particle or a wave?), the Schrödinger's cat (is it dead or alive?), and the Heisenberg's uncertainty principle (where and how fast is it?).
"As a consequence, it was soon
understood that quantum systems should be interrogated in their own specific
language, eventually provided by modern quantum theory. It is then pertinent to
address the possibility of interrogating classical systems with questions
inspired by quantum physics. This is what we did, indeed, finding that
classical systems with an underlying wave mechanism answer these questions in
the same way truly quantum systems do. But one has to choose your system
carefully: one would not be able to make it by using plain balls, for
instance."

In the future, the physicists plan
to investigate how the universal bounds might emerge in the first place.

"Our results show that the
'quantum' bounds are common to many physical theories," said coauthor Adán
Cabello at the University of Sevilla. "This suggests that the reason for
these bounds is something very simple and arguably inherent to the kind of
theories we are interested in: theories in which 'measurements' produce
repeatable results which are not affected by some other measurements.

"Surprisingly, this simple idea
singles out many 'quantum' bounds. When we adopt this perspective, what is
really significant is the fact that these bounds are actually reachable in
nature. This shows that no hypothetical physical principle is acting and leads
us to the conjecture that one of the physical principles that singles out
quantum theory is precisely that one: There is no principle determining the
probabilities of the outcomes of these 'measurements.'

"One plan is to prove that this
simple idea is responsible for all quantum bounds. Another plan is to test
whether it is really true that these bounds can be reached with quantum
systems. So far, and only very recently, H. S. Poh

*et al*. have confirmed the so-called Tsirelson bound, 2√2, with four significant digits, but there is absolutely no experimental evidence of whether we can 'touch' these bounds in other scenarios. Also, it would be great to derive quantum theory from the assumption that there are no laws of nature determining or limiting the probabilities of measurement outcomes, and that the whole machinery of the theory follows from the aesthetic preference in the way we define 'measurements.'"
Finally, the physicists also plan to
investigate potential applications, such as building quantum technologies with
the help of classical systems.

"Although inefficient in the
sense that they require more memory or space, classical systems are sometimes
better to produce 'quantum' numbers than quantum systems themselves,"
Frustaglia said. "In contrast to quantum systems, which are very sensitive
to the environment, the wires in our experiment can be bent, moved, heated,
etc., and the results are the same. This suggests a future in which quantum
technologies are actually built using quantum systems plus classical systems
imitating quantum systems. It also raises the question as to whether similar
'quantum' features with potential functionalities can emerge in other supports
as complex networks of artificial or biological nature. An appropriate answer
to this questions requires multidisciplinary efforts that we are presently
considering."

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