The fabulous story of quantum entanglement

The 2022 Nobel Prize in Physics was awarded to three specialists in quantum entanglement, including the Frenchman Alain Aspect. The experiment he conducted with his team at the Institut d'Optique in Orsay in 1982 was recognized as groundbreaking by the scientific community. It provided proof that quantum mechanics, despite its strangeness and probabilistic formalism, is a complete theory; that is, a theory that fully accounts for reality as it is, thus proving Albert Einstein wrong. But the significance of this experiment doesn't stop there: it laid the seeds for the quantum computer. Let's dive into this intellectual adventure full of twists and turns!

In the 1930s, the Bohr-Einstein debate on the formalism of quantum mechanics gave rise to one of the most perplexing hypotheses in physics: quantum entanglement. This was experimentally validated by Aspect in 1982.

The 1920s saw the emergence in the study of atoms and elementary particles of a new formalism, quantum mechanics, of very high operational efficiency but which calls into question the way of understanding reality.

The fundamental strangeness of this theory is the principle of quantum superposition. It states that a particle can be in two different places at once (position 1 AND position 2), with a probability of being present in each of these places; for example, a 50% probability of being in position 1 and 50% in position 2. It is only when the particle is observed through a measuring instrument that it "chooses" one of the possible positions (position 1 OR position 2). Before observation, the superimposed particle has no precise location. During measurement, the particle "fixes" itself in a position predicted by the theory.

This represents a true break with classical physics, which attributes to every system properties—such as position and velocity—that are inherent to it, independent of their measurement. If a reckless driver's car is caught speeding at 140 km/h, there's no doubt it would have been traveling at the same speed at the same instant if there hadn't been a speed camera. Quantum mechanics takes a completely different approach, where it is the measurement, or more precisely the perturbation produced by the measurement, that "forces" the particle to select a value from among those possible (calculated by the theory).

Photo of a twin radar. The (obviously imaginary) application of quantum superposition to the macroscopic world allows us to grasp its strangeness. In fact, a car traveling on a highway would not have a well-defined speed, it would have several at the same time... before the observer's twin radar (the police officer) forces the car to choose a speed (80 km/h). In classical physics, measurement is much more neutral: the car has its own speed (80 km/h) and the twin radar simply indicates the speed at which it is traveling. Measurement is equivalent to reading an intrinsic property of the observed object without disturbing it.

The interpretation of quantum mechanics became a source of epistemological debate regarding how to consider reality and the act of becoming aware of it through measurement. Two giants of physics clashed on this subject: the German-born Swiss-American Albert Einstein on one side, and the Dane Niels Bohr on the other. The standard interpretation (also known as the Copenhagen interpretation) of quantum mechanics, established by Bohr, notably defends the idea that randomness is intrinsic to the infinitely small. This probabilistic aspect (" God does not play dice "), but also the fact that observation so significantly alters the observed object (" I like to think that the moon is the same even if I don't look at it "), intellectually challenged Einstein… The father of special and general relativity believed that quantum mechanics, although very effective in its results, was an incomplete theory.

Einstein remained convinced that a fundamental theory in physics could not be probabilistic and that quantum mechanics only revealed a part of reality, the latter possessing an underlying component that the theory did not account for. Knowledge of these elements of reality would complete the theory and render it deterministic.

The EPR paradox

In May 1935, when quantum mechanics was well established, Einstein and two colleagues from Princeton University, Boris Podolsky and Nathan Rosen, published a thought experiment now known as the "EPR paradox" (Einstein-Podolsky-Rosen). The EPR argument came as a bombshell, highlighting a "paradox" in the Copenhagen interpretation!

This article presents two particles, A and B, emitted from the same source. The authors consider the particles to be "entangled," meaning they are prepared in a specific state such that at every instant their velocities are equal and their positions are opposite relative to the source. It's worth noting that this (very strong) connection between systems A and B isn't a random occurrence; it's made possible by quantum mechanics, specifically the Schrödinger equation. Let's continue the experiment… We measure the position of A. According to the theory, it settles at a particular position. But since B is entangled with A, we can determine its position without making any measurements: it is exactly opposite to A with respect to the source. And this is where the paradox arises, because the Copenhagen interpretation stipulates that B is in a superposition state before any measurement and that its position is therefore unknown, which is not the case here!

The EPR paradox. Two entangled particles are emitted from a source (S). By measuring the position of the particle on the right (position 1), we can immediately deduce the position of the particle on the left (position 2) without taking any measurements. In fact, position 2 = - position 1 (relative to S). However, knowing a property of a particle without measuring it is contrary to the Copenhagen interpretation. Credits: YouTube channel « Photons jumeaux »

The EPR article states that if one is able to determine with absolute certainty the value of a physical quantity of particle B without measuring it, that is, without disturbing it, then this means that there are unknown elements of reality ("hidden variables") shared between particles A and B. Einstein, Podolsky and Rosen add that if a theory is complete, it must take into account all the hidden variables related to the source and carried by A and B.

We know that every quantum measurement causes a perturbation, but this does not mean that the absence of measurement guarantees the absence of perturbation, at least not in the EPR experiment. There could indeed be an unknown mechanism that perturbees particle B at a distance, following the measurement performed on A. In this case, particle B would be perturbed by the measurement performed on A—instantaneously, regardless of the distance between A and B, according to quantum formalism. EPR rejects this hypothesis because it directly contradicts special relativity, which postulates that nothing can travel faster than light.

The EPR argument is a solid attack against the Copenhagen interpretation. Niels Bohr's defense will consist of recalling the postulates of quantum mechanics and stating that the two entangled particles cannot be separated, that they must be considered as part of a whole, thus postulating non-locality (or non-separability) and safeguarding special relativity… As expected, the answer does not satisfy Albert Einstein. This debate, more philosophical than anything else and which does not call into question the results of quantum mechanics, interests neither physicists nor engineers and falls into oblivion.

Bohm's simplification

In the early 1950s, physicist David Bohm dusted off the EPR paper and simplified the thought experiment: the particles became photons (particles of light), and it was no longer the position that was being measured, but the polarization. What is this all about?

Without going into detail, polarization is a property specific to the photon. Its measurement can take two opposite values, horizontal or vertical, like the heads or tails of a coin toss. We can already see the simplification of the initial thought experiment: from a multitude of potential positions that a particle can have, we reduce here to two the number of states to measure, a horizontal polarization or a vertical polarization. The mathematical representation of the EPR situation is thus simplified, and its experimentation more feasible in the laboratory.

Polarization is measured using an optical filter called a polarizer. The instrument can be oriented at various angles. A horizontally positioned polarizer will allow horizontally polarized photons to pass through and vertically polarized photons to be reflected. And vice versa. A polarizer has two output channels: one for the unaltered photons, and the other for the reflected photons. Simply placing a photon detector opposite each output channel determines whether a photon is horizontally or vertically polarized.

Measurement of a superimposed photon in polarization: A superimposed photon with two opposite polarizations, horizontal AND vertical, travels toward a vertically oriented polarizer (Figure 1). At the moment of encounter between the photon and the measuring instrument, the photon adopts, according to quantum mechanics, a precise polarization value: horizontal OR vertical. There is a 50% chance that the polarization will be horizontal and therefore the same chance that it will be vertical. As the polarizer is oriented vertically, if the photon settles on vertical polarization, it exits through the “transmitting” path of the polarizer and will be detected by the right-hand detector (Figure 2); otherwise, the photon exits through the “non-passive” path of the polarizer and will be detected by the left detector (Figure 3). Credits: YouTube channel « Photons jumeaux »

Consider a source that emits superimposed photons. Just as superimposed particles can have several distinct positions at once , superimposed photons can have both horizontal and vertical polarization simultaneously . It is only when measured through a polarizer that the photons adopt a precise polarization: either horizontal or vertical. We also assume that the photons are in superposition states such that quantum mechanics tells us that, for each photon, there is a 50% chance of obtaining horizontal polarization and the same percentage of obtaining vertical polarization during measurement.

Let's see how, with all these elements, David Bohm revisited the EPR experiment. Imagine a source emitting pairs of entangled photons superimposed horizontally and vertically, and whose polarization we want to measure. On the emission axis, and on either side of the source, we install a polarizer identically oriented (for example, vertically) to the other. On each polarizer, there is a 50% chance of measuring horizontally polarized photons and the same probability of measuring vertically polarized photons.

However, if we consider the two polarizers together, quantum mechanics predicts the following oddity (already seen above with the identical positions of the entangled particles in the original EPR experiment): the photon measurements taken by one polarizer are exactly the same as those taken by the other. Although random at the output of each polarizer, the photon polarization measurements are perfectly correlated: either both are horizontal or both are vertical. To return to the coin toss analogy, it's as if we had two experimenters each tossing a coin, heads or tails, simultaneously. At the level of each tosser, there is indeed a 50/50 chance of getting heads or tails. But if one of the experimenters gets heads, the other necessarily gets heads as well – and therefore if they get tails, the other gets tails. Strange, isn't it?

The EPR experiment revised and simplified by David Bohm: The source emits a pair of entangled photons superimposed in horizontal (H) and vertical (V) polarization. The photons each travel toward a vertically oriented polarizer (Figure 1). Quantum mechanics predicts a remarkable measurement result: although random at the output of each polarizer (either H at 50% or V at 50%), the photon polarization measurements are perfectly correlated: either HH (Figure 2) or VV (Figure 3). HV and VH measurements are excluded by theory. EPR measurements are perfectly random locally, but absolutely correlated globally. Credits: YouTube channel « Photons jumeaux »

With this reworking of the original EPR experiment, David Bohm further highlights one of the most surprising results of entanglement: the perfect correlation between two distinct and random measurements, as if the objects to which they relate could not be separated. But Bohm does not believe in the non-locality of reality; he is convinced that these correlations at a distance must be explained differently, bringing back to the forefront the hidden variables postulated by Einstein.

Bell's inequalities

It would be another fifteen years or so before John Bell, an Irish physicist at CERN, turned his attention to a simplified version of the EPR paradox. Like Einstein and Bohm, Bell was also convinced that the formalism of quantum mechanics was incomplete. He believed that there existed a set of hidden variables shared at the source by the two entangled photons, which each carried with it as it moved away. Thus, the polarization properties of the two photons would be established from the very beginning of the experiment, and not at the moment of their measurement.

To understand the perspective of those who believe in hidden variables, imagine two identical twins whom no one knows. No one knows they share the same DNA (the hidden variables). One twin lives in Paris and the other in Brussels… The knowledge of the eye color of the Parisian twin by a local observer is not transmitted instantly over a distance to the eyes of the Brussels twin…

However, in 1964, to his great surprise, Bell demonstrated the opposite result. More precisely, he mathematically proved that any theory with hidden variables is incompatible with the results of quantum mechanics, thus vindicating Bohr and his Copenhagen interpretation against Einstein. Bell's theorem, from which Bell's inequalities would later derive, ended the theoretical debate between the two physicists: quantum physics is indeed a complete and non-local theory (two entangled photons cannot be separated, however distant they may be). How did he do it?

John Bell at CERN in 1982. His famous theorem demonstrates one of the most spectacular results in 20th-century physics: quantum non-locality (or non-separability), which states that if two particles are entangled, then any action on one (e.g., a measurement) instantly affects the other. Even if the two particles are separated by an astronomical distance, such as several million light years... The theorem also sowed the seeds of quantum computing. Image: CERN

Bell's idea was to approach the problem statistically: he revisited David Bohm's experiment, focusing on the coincidence rate between detectors. Coincidence occurs when two entangled photons emerge from the same side of the polarizers. Since the photons have the same polarity when measured, when the two polarizers are oriented horizontally, the coincidence rate is 100%. The same is true when they are oriented vertically. And for the same reason, if one polarizer is oriented vertically and the other horizontally, the coincidence rate drops to 0%. Bell thus calculated a certain quantity, which depends on a set of coincidence rates obtained for different angles of inclination of one polarizer relative to the other.

In a hidden-variable model (the most general possible), he demonstrates that this quantity is necessarily less than or equal to 2 (one of Bell's famous inequalities). However, quantum mechanics gives a value close to 2.8! This is why quantum mechanics is said to violate Bell's inequalities. He thus proves the incompatibility between the hidden-variable model and quantum mechanics. Since the latter has been solidly proven in practice, the hidden-variable hypothesis is somewhat weakened, if not invalidated.

But physics is first and foremost an experimental science. Therefore, we must set up the EPR experiment in the laboratory – according to the design envisioned by Bell, similar to Bohm's – and observe what happens: a (very likely) violation of Bell's inequalities. The Irish physicist will not carry out this experiment, because the technological means of the late 1960s were insufficient to perform this type of experimentation.

Aspect's Experience

In 1974, Alain Aspect, a young French physicist at the Institut d'Optique in Orsay, passionate about the subject, decided to embark on this adventure. With limited resources, it took him nearly eight years to finally carry out, in 1982, an experiment reproducing Bell's fundamental principle. Alongside his colleagues, Philippe Grangier, Jean Dalibard, and Gérard Roger, he observed (as predicted by John Bell) the violation of the eponymous inequalities. He experimentally proved, irrefutably, the non-separability of entangled photon pairs, thus refuting Albert Einstein's hidden variable hypothesis.

Alain Aspect in his laboratory at the Institut d'Optique in Orsay in 1984. Alain Aspect and his team were the first to conduct an experiment similar to the one imagined by John Bell. He demonstrated the violation of Bell's inequalities, proving that quantum physics is a complete and non-local theory (entangled particles cannot be separated, no matter how distant they are), contrary to what Albert Einstein believed. Image: SCIENCES ET AVENIR

A look at one of the most famous theoretical physics experiments of the 20th century!

First, the challenge was to create a reliable source capable of emitting entangled photon pairs. The Orsay team used calcium atoms excited by two different krypton lasers. Through an effect known as "atomic cascade," the calcium atom de-excites, emitting a pair of entangled photons. Aspect and his colleagues spent nearly five years developing this source! The photon emission system is a true technological marvel, enabling a detection rate of 100 photons per second, for a maximum experimental time of only 100 seconds—it is indeed important that the experiment be brief to minimize phenomena that could skew the results.

Next, to get as close as possible to the "ideal" experiment envisioned by Bell—that is, to minimize any possible correlations between the source of entangled photons and the polarizers—the latter had to rotate at the very last moment. In any case, after the photons were emitted and before their polarization was measured. The polarizers in the Orsay experiment were 6 meters from the source. The time it takes a photon to travel 6 meters (at the speed of light) is approximately 20 nanoseconds. How could one change the orientation of a glass and metal apparatus (the polarizers of the time) in such a tiny span of 20 billionths of a second? Impossible!

This was without taking into account the ingenious Alain Aspect, who then conceived the idea of using a switching mechanism that alternately sends photons of light onto two polarizers oriented differently, the entire device essentially functioning as a single rotating polarizer. To achieve this switching, Aspect designed, had built, and patented water-based switchers equipped with piezoelectric transducers, deflecting the photons passing through them either towards one polarizer or the other.

(Highly simplified) diagram of the setup for Aspect's experiment conducted in 1982, which closely resembles the “ideal” experiment imagined by John Bell in 1964. Shown here are: the two laser guns generating (in the center) the pair of entangled photons, the water deflectors and their two differently oriented polarizers, and finally the photon detectors. Credits: YouTube channel « Photons jumeaux »

After several months of fine-tuning and adjusting all the equipment in the setup, the experiment was finally launched. The results exceeded the expectations of Aspect and his team: the Bell quantity produced by the experiment was equal to 2.7 – clearly violating Bell's inequality and approaching the value of 2.8 given by quantum mechanics.

The scientific community applauds the technical quality and rigor of the experiment. It hails Aspect's experiment, the first of its kind, as irrefutable proof of the non-locality hypotheses at work within entangled particles, in accordance with John Bell's theoretical prediction of 1964. Aspect's experiment also proves that quantum physics is a complete theory, as Niels Bohr supposed in his debate with Albert Einstein during the 1930s (it accurately accounts for the infinitely small as it is).

In the history of science, quantum entanglement is truly unique. It began with a remarkable thought experiment (Einstein-Podolsky-Rosen), led to a brilliant mathematical theorization (Bell), and culminated in a high-level physics experiment (Aspect). And the adventure may only be beginning… because quantum entanglement and superposition are the building blocks of quantum computers, still conceptual or in their embryonic stage, but which some predict will be operational within a few years…

This text is the result of an automated translation. The first version of this text (in French) is available at the following address:

https://www.chroniquesplurielles.info/post/la-fabuleuse-histoire-de-l-intrication-quantique

Sources :

Le chat de Schrödinger, prélude à l’ordinateur quantique https://www.chroniquesplurielles.info/post/le-chat-de-schr%C3%B6dinger-superstar

Intrication Quantique (1/4) : Le débat Bohr-Einstein

https://www.youtube.com/watch?v=gOQGkIVxv3w

Intrication Quantique (2/4) : Les inégalités de Bell

https://www.youtube.com/watch?v=xduUcFflYX0

Intrication Quantique (3/4) : Les expériences d’Aspect

https://www.youtube.com/watch?v=SIwN9T010Tg

Le prix Nobel de physique 2022 pour l’intrication quantique https://theconversation.com/le-prix-nobel-de-physique-2022-pour-lintrication-quantique-133000

Les cinquante ans du théorème de Bell

https://home.cern/fr/news/news/physics/fifty-years-bells-theorem

L’intrication quantique, ou le rêve de la communication instantanée https://www.sciencepresse.qc.ca/blogue/flashcordon/2013/06/24/intrication-quantique-reve-communication-instantanee

Expérience d’Aspect

https://fr.wikipedia.org/wiki/Exp%C3%A9rience_d%27Aspect

Le prix Nobel de physique 2022répond à nos questions https://www.youtube.com/watch?v=e-tD6n4aOgg