**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.^{[2,4,5]}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*.

DOI: 10.1103/PhysRevLett.127.120401

Does that mean there is no such thing as a fair coin?

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.

A simple argument to explain this transition from quantum mechanics to classical mechanics is the coarse-graining mechanism: 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 leads to the principle of macroscopic locality. Similarly, temporal quantum correlations reduce to classical correlations (macroscopic realism) and quantum contextuality reduces to macroscopic non-contextuality.

It was strongly believed that the quantum-to-classical transition is universal, although a general proof was missing.

For example, when performing random coin tosses

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.

Does that mean there is no such thing as a fair coin?

of course it does not mean we cant have a coin fair

lets start one here to offer a practical proof for bohr 1920

i bring you my latest conjuring trick as you read this toss a coin in the air

how many quark lepton muon have you launched in the air

the length of femtosecond time ago

4,320,000,000 ??????ago = 2 minutes ago

well i launched mine also i tossed my coin into the air

so your coin a with quark lepton and muon

and my coin b with quark lepton and muon

and alices coin and bobs coin c and d with quarks and leptons and muons

so where are we in space and time i ask u

you me alice bob

quark lepton muon a b c d

location location

12.00 noon your location my location hers his

your coin is 2 metres in the air from you person

15.00 pm your location my location hers his

your coin is in your pocket on your person

18,00 pm ditto ditto ditto ditto

your coin is in your pocket on your person

21.00 pm ditto ditto ditto ditto

your coin is in your pocket on your person

24.00 pm midnight your coin is lying on a chair in the pocket of your clothing

now if you believe that you are living in cloud coo coo land

so think again and tell me what has happened

so lets begin again for my next trick of the plain light

12.00 noon your coin is 2 metres in the air from your person

18.00 pm your coin is in your pocket on your person

as the two coins have revolved on the surface of the earth globe

a and b c d have moved 4500 kilometres from 12 noon location

but 6030 in real time from 12 noon at 52 degrees north latitude

now if you believe that

you are getting close but not close enough to the truth

so lets go to midnight on the far side of the globe

12.00 noon your coin is 2 metres in the air from your person

24.00 pm midnight your coin is lying on a chair in the pocket of your clothing

a and b c d have moved 9,000 kilometres from 12 noon location

we were at noon we have traveled across the earth globe diameter 6,000 kilometres = midnight

we are apart 6,000 kilometres from 12 noon

but but but

a and b c d are 52 north latitude location

and according to spin tronics with a 23 earth planet tilt

at noon we both face upwards looking at the sun

at midnight we both face downward looking at the stars

so we are horizontally on a lower plane 18,000 kilometres travelled but 12,000 kilometres apart from our noon location

a couple of degree below 52 degrees north at noon

a day in the life of a quark lepton muon and bit of mustard mark are you having a drink too

thats not the end of the story but it will do for now

hence our proof to bohr of quantum effects working at macro scales all numbers approximates

from the classical to the classical quantum state

It seems to me that some of those Hindu gurus and some other holy people may have mastered the art of perception of macro quantum physics effects without giving it that name.