Imagine a magician taking two coins, rubbing them together and giving you one with the words: “I will flip my coin and it will show heads or tails. Whenever and wherever you flip your coin for the first time, it will show the same.” Can there really be such a magical connection between objects? The answer is yes – in quantum physics. The magical connection is called entanglement, a term coined by Erwin Schrödinger. Today entanglement is seen to be the outstanding property of quantum systems.
In 1935 Einstein, Podolsky and Rosen (EPR) published a paper describing what later became known as the “EPR paradox”. In the paper they describe entangled pairs of particles. Particles are entangled if they were generated together or interacted with each other, for example in a collision. They then share common properties, for example “position” or “momentum”. However, the distribution of these properties among the entangled particles is not defined by the quantum physical formalism. The property of one particle is only defined once a measurement is carried out on it, with this very property then being simultaneously defined for the other entangled particle, however distant they are apart. EPR, however, reject such an instantaneous connection; they propose a local realistic description of nature and claim that the formalism of quantum physics is incomplete. EPR assume that there is a yet unknown more complete description of nature, referred to as “hidden variables”.
In 1964, John Bell (Figure 1) found proof that the effects predicted for entanglement could not be explained on the basis of local realism. His proof is based on what is called “Bell’s inequality”. “Local” in this context means that mutual influence cannot occur faster than at light speed. “Realism” denotes that physical properties do exist regardless of whether they are measured or not. Therefore, only experiments could bring about a decision: Either the quantum physical predictions are wrong or there is an instantaneous connection between entangled particles. Einstein called this “spooky action at a distance” and rejected it resoundingly. However, if the results of the experiments violate a Bell’s inequality, then no local realistic description of nature is possible.
The first experiments on this were carried out in the US in the 1970s by John Clauser et al. Then, in the 1980s, a French group around Alain Aspect was able to clearly demonstrate that Bell’s inequalities were violated – much to the astonishment of Bell himself. Later other groups – in particular those around Anton Zeilinger in Austria – improved the experiments and closed existing loopholes in the proof. Since the 1980s the results of the experiments support the quantum physical prediction.
An entanglement experiment
A simplified experiment on quantum entanglement is shown in Figure 2. There are crystals which convert single high-energy photons into two low-energy polarization-entangled photons. One type of this entanglement is that both photons must have parallel polarizations. When excited by a laser this crystal emits entangled photon pairs with a superposition of horizontal and vertical polarization. Due to the superposition the polarization is not fixed as long as it is not measured, although each photon pair is definitely parallel-polarized.
The source in Figure 2 emits the entangled photon pairs to the right and to the left. The superposition of the polarization is symbolized by Schrödinger’s cat. The entanglement is symbolized by the dashed loop. If we only investigate one side of the experiment (with and without polarizer), we will find that on average every second photon passes through the polarizer, regardless of the angle in which we turn the polarizer. That is not surprising.
The big surprise comes when we compare both sides of the experiment: If the two polarizers are aligned to be parallel, whenever a photon goes through the polarizer on the left, a photon also goes through the polarizer on the right. This is true for every possible angle in which we turn the two polarizers. The distance between the polarizers and the source can be any size; it can be the same for both or different. As on average only every second photon goes through the polarizer and it is random for each single photon whether it goes through or not, this 100 % correlation is truly astounding.
A Bell’s inequality applied
The quantum physical formalism predicts this perfect correlation but gives no evidence to explain how this is possible. A local realistic explanation using hidden variables would be that the source gives every photon exact rules on how it must behave at the polarizer. However, Bell found out that such explanations do not work when investigating correlations which are less than 100 %. To achieve that in the experiment we rotate the polarizers relatively to each other. In a humorous essay  from 1980 Bell used the following inequality as proof. This inequality essentially states that a part cannot be larger than the whole to which it contributes. To show that, it can be easily proved that the right side of this Bell’s inequality forms part of the left side.
The inequality contains the probabilities p of three pairs of events. In our experiment, A means that a photon goes through the 0° polarizer. B means that it goes through the polarizer turned by 30°, and C means that it goes through the polarizer turned by 60°. A horizontal line at the top means that the photon does not go through the polarizer. For example: p(AB) is the probability that the left photon goes through the 0° polarizer but the right photon does not go through the polarizer turned by 30°.
Now we turn the polarizers for each of the three event pairs, as defined above, and determine the relative frequency with which the left photon goes through and the right photon does not. If we repeat the measurements often enough the relative frequencies approximate the probabilities predicted by quantum physics. p(AB) = 1/4 means, for example, that in one quarter of the cases the right photon does not go through whereas in three quarters of the cases both photons go through. The quantum physical calculation and the experiment come to similar results:
Bell’s inequality is violated because the right side is larger than the left side. That means that the correlation between the entangled photons is stronger than can be explained on the basis of local realism. Consequently, the behavior of the entangled photons cannot be defined by the source. Instead there must be a connection between the entangled photons which defines and aligns the polarization of both photons when the first photon meets the polarizer. There is also a “Bell game” which demonstrates the necessity of this connection: There is no strategy with which the two players or two arbitrarily powerful computers can violate Bell’s inequality and win the game if they are not allowed to reconcile after receiving the questions.
In the quantum physical formalism the alignment of the entangled particles is instantaneous. In 2008, experiments by Nicolas Gisin in the Swiss telephone glass fiber network found that the alignment of entangled photons occurred at a speed at least 10,000 times faster than light speed. The entanglement therefore causes an instantaneous alignment across any distance. The “spooky action at a distance” therefore exists and, according to current knowledge, the quantum physical formalism describes everything which can be said about nature. The latter was proposed by Niels Bohr as early as 1935 in his response to the EPR paper.
Today the entanglement of quantum objects is used in exciting ways: Tap-proof communication via quantum cryptography, quantum teleportation and first quantum computers have already been implemented. Entanglements also seem to form the currently still poorly understood interface between the ambiguous quantum world and the world we experience, which presents itself so unambiguously. For this reason, the detection of photons in analytical instruments such as the Litesizer™ 500 from Anton Paar is very probably based on entanglement. However, one question remains unanswered: How does nature accomplish entanglement, this magical connection between objects over space and time? In response, the magician smiles enigmatically and disappears into thin air.
 Bell, J.S.: Bertlmann’s Socks and the Nature of Reality, CERN 1980. https://cds.cern.ch/record/142461/files/198009299.pdf