Scientists from the University of Vienna and the Austrian Academy of
Sciences have shown that it is possible to fully preserve the mathematical
structure of quantum theory in the macroscopic limit.

One of the most fundamental features of quantum physics is Bell nonlocality:
the fact that the predictions of quantum mechanics cannot be explained by
any local (classical) theory. This has remarkable conceptual consequences
and far-reaching applications in quantum information. However, in our
everyday experience, macroscopic objects seem to behave according to the
rules of classical physics, and the correlations we see are local. Is this
really the case, or can we challenge this view?

In a recent paper in Physical Review Letters, scientists from the University
of Vienna and the Institute of Quantum Optics and Quantum Information
(IQOQI) of the Austrian Academy of Sciences have shown that it is possible
to fully preserve the mathematical structure of quantum theory in the
macroscopic limit. This could lead to observations of quantum nonlocality at
the macroscopic scale.

Our everyday experience tells us that macroscopic systems obey classical
physics. It is therefore natural to expect that quantum mechanics must
reproduce classical mechanics in the macroscopic limit. This is known as the
correspondence principle, as established by Bohr in 1920.[1]

A simple argument to explain this transition from quantum mechanics to
classical mechanics is the coarse-graining mechanism:[2] if measurements performed on macroscopic systems have limited
resolution and cannot resolve individual microscopic particles, then the
results behave classically. Such an argument, applied to (nonlocal) Bell
correlations,[3] leads to the principle of macroscopic locality.[4] Similarly, temporal quantum correlations reduce to classical
correlations (macroscopic realism)[2] and quantum contextuality reduces to macroscopic
non-contextuality.[5]

It was strongly believed that the quantum-to-classical transition is
universal, although a general proof was missing. To illustrate the point,
let us take the example of quantum nonlocality. Suppose we have two distant
observers, Alice and Bob, who want to measure the strength of the
correlation between their local systems. We can imagine a typical situation
where Alice measures her tiny quantum particle and Bob does the same with
his and they combine their observational results to calculate the
corresponding correlation.

Since their results are inherently random (as is always the case in quantum
experiments), they must repeat the experiment a large number of times to
find the mean of the correlations. The key assumption in this context is
that each run of the experiment must be repeated under exactly the same
conditions and independently of other runs, which is known as the IID
(independent and identically distributed) assumption. For example, when
performing random coin tosses, we need to ensure that each toss is fair and
unbiased, resulting in a measured probability of (approximately) 50% for
heads/tails after many repetitions.

Such an assumption plays a central role in the existing evidence for the
reduction to classicallity in the macroscopic limit.

^{[2,3,5]}However, macroscopic experiments consider clusters of quantum particles that are packed together and measured together with a limited resolution (coarse-graining). These particles interact with each other, so it is not natural to assume that correlations at the microscopic level are distributed in units of independent and identical pairs. If so, what happens if we drop the IID assumption? Do we still achieve reduction to classical physics in the limit of large numbers of particles?
In their recent work, Miguel Gallego (University of Vienna) and Borivoje
Dakić (University of Vienna and IQOQI) have shown that, surprisingly,
quantum correlations survive in the macroscopic limit if correlations are
not IID distributed at the level of microscopic constituents.

“The IID assumption is not natural when dealing with a large number of
microscopic systems. Small quantum particles interact strongly and quantum
correlations and entanglement are distributed everywhere. Given such a
scenario, we revised existing calculations and were able to find complete
quantum behavior at the macroscopic scale. This is completely against the
correspondence principle, and the transition to classicality does not take
place”, says Borivoje Dakić.

By considering fluctuation observables (deviations from expectation values)
and a certain class of entangled many-body states (non-IID states), the
authors show that the entire mathematical structure of quantum theory (e.g.,
Born’s rule and the superposition principle) is preserved in the limit. This
property, which they call macroscopic quantum behavior, directly allows them
to show that Bell nonlocality is visible in the macroscopic limit.

“It is amazing to have quantum rules at the macroscopic scale. We just have
to measure fluctuations, deviations from expected values, and we will see
quantum phenomena in macroscopic systems. I believe this opens the door to
new experiments and applications,” says Miguel Gallego.

### Notes

- Bohr, N. (1920). Über die Serienspektra der Elemente. Zeitschrift für Physik, 2 (5), 423-469.
- Kofler, J., & Brukner, Č. (2007). Classical world arising out of quantum physics under the restriction of coarse-grained measurements. Physical Review Letters, 99 (18), 180403.
- Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics Physique Fizika, 1 (3), 195.
- Navascués, M., & Wunderlich, H. (2010). A glance beyond the quantum model. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466 (2115), 881-890.
- Henson, J., & Sainz, A. B. (2015). Macroscopic noncontextuality as a principle for almost-quantum correlations. Physical Review A, 91(4), 042114.

## Reference:

Macroscopically Nonlocal Quantum Correlations by Miguel Gallego and Borivoje
Dakić, 16 September 2021, Physical Review Letters.

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