Quantum entanglement and wormholes may be closely related. Quantum entanglement in simple words

There have been many popular articles talking about quantum entanglement. Experiments with quantum entanglement are very impressive, but have not received any prizes. Why are such experiments interesting for the average person not of interest to scientists? Popular articles talk about the amazing properties of pairs of entangled particles - impact on one leads to an instant change in the state of the second. And what is hidden behind the term “quantum teleportation”, which has already begun to be said that it occurs at superluminal speed. Let's look at all this from the point of view of normal quantum mechanics.

What comes from quantum mechanics

Quantum particles can be in two types of states, according to the classic textbook by Landau and Lifshitz - pure and mixed. If a particle does not interact with other quantum particles, it is described by a wave function that depends only on its coordinates or momenta - this state is called pure. In this case, the wave function obeys the Schrödinger equation. Another option is possible - the particle interacts with other quantum particles. In this case, the wave function refers to the entire system of interacting particles and depends on all their dynamic variables. If we are interested in only one particle, then its state, as Landau showed 90 years ago, can be described by a matrix or density operator. The density matrix obeys an equation similar to the Schrödinger equation

Where is the density matrix, H is the Hamiltonian operator, and the brackets denote the commutator.

Landau brought him out. Any physical quantities related to a given particle can be expressed through the density matrix. This condition is called mixed. If we have a system of interacting particles, then each of the particles is in a mixed state. If the particles scatter over long distances and the interaction disappears, their state will still remain mixed. If each of several particles is in a pure state, then the wave function of such a system is the product of the wave functions of each of the particles (if the particles are different. For identical particles, bosons or fermions, it is necessary to make a symmetric or antisymmetric combination, see, but more on that later. The identity of particles, fermions and bosons is already a relativistic quantum theory.

An entangled state of a pair of particles is a state in which there is a constant correlation between physical quantities belonging to different particles. A simple and most common example is that a certain total physical quantity is conserved, for example, the total spin or the angular momentum of a pair. In this case, a pair of particles is in a pure state, but each of the particles is in a mixed state. It may seem that a change in the state of one particle will immediately affect the state of another particle. Even if they are scattered far away and do not interact, this is what is expressed in popular articles. This phenomenon has already been dubbed quantum teleportation. Some illiterate journalists even claim that the change occurs instantly, that is, it spreads faster than the speed of light.

Let's consider this from the point of view of quantum mechanics. Firstly, any impact or measurement that changes the spin or angular momentum of only one particle immediately violates the law of conservation of the total characteristic. The corresponding operator cannot commute with full spin or full angular momentum. Thus, the initial entanglement of the state of a pair of particles is disrupted. The spin or momentum of the second particle can no longer be unambiguously associated with that of the first. We can look at this problem from another angle. After the interaction between particles has disappeared, the evolution of the density matrix of each particle is described by its own equation, in which the dynamic variables of the other particle are not included. Therefore, the impact on one particle will not change the density matrix of the other.

There is even Eberhard's theorem, which states that the mutual influence of two particles cannot be detected by measurements. Let there be a quantum system that is described by a density matrix. And let this system consist of two subsystems A and B. Eberhard’s theorem states that no measurement of observables associated only with subsystem A does not affect the result of measurement of any observables that are associated only with subsystem B. However, the proof of the theorem uses the wave reduction hypothesis a function that has not been proven either theoretically or experimentally. But all these arguments were made within the framework of non-relativistic quantum mechanics and relate to different, non-identical particles.

These arguments do not work in relativistic theory in the case of a pair of identical particles. Let me remind you once again that the identity or indistinguishability of particles comes from relativistic quantum mechanics, where the number of particles is not conserved. However, for slow particles we can use the simpler apparatus of nonrelativistic quantum mechanics, simply by allowing for the indistinguishability of the particles. Then the wave function of the pair must be symmetric (for bosons) or antisymmetric (for fermions) with respect to the permutation of particles. Such a requirement arises in relativistic theory, regardless of particle velocities. It is this requirement that leads to long-range correlations between pairs of identical particles. In principle, a proton and an electron can also be in an entangled state. However, if they diverge by several tens of angstroms, then interaction with electromagnetic fields and other particles will destroy this state. Exchange interaction (as this phenomenon is called) acts at macroscopic distances, as experiments show. A pair of particles, even having separated by meters, remains indistinguishable. If you make a measurement, then you do not know exactly which particle the measured value belongs to. You are taking measurements on a couple of particles at the same time. Therefore, all spectacular experiments were carried out with exactly the same particles - electrons and photons. Strictly speaking, this is not exactly the entangled state that is considered within the framework of non-relativistic quantum mechanics, but something similar.

Let's consider the simplest case - a pair of identical non-interacting particles. If the velocities are small, we can use nonrelativistic quantum mechanics, taking into account the symmetry of the wave function with respect to the permutation of particles. Let the wave function of the first particle , the second particle - , where and are the dynamic variables of the first and second particles, in the simplest case - just coordinates. Then the wave function of the pair

The + and – signs refer to bosons and fermions. Let's assume that the particles are far away from each other. Then they are localized in distant regions 1 and 2, respectively, that is, outside these regions they are small. Let's try to calculate the average value of some variable of the first particle, for example, coordinates. For simplicity, we can imagine that the wave functions include only coordinates. It turns out that the average value of the coordinates of particle 1 lies BETWEEN regions 1 and 2, and it coincides with the average value for particle 2. This is actually natural - the particles are indistinguishable, we cannot know which particle has the coordinates measured. In general, all average values ​​for particles 1 and 2 will be the same. This means that by moving the localization region of particle 1 (for example, the particle is localized inside a defect in the crystal lattice, and we move the entire crystal), we influence particle 2, although the particles do not interact in the usual sense - through an electromagnetic field, for example. This is a simple example of relativistic entanglement.

There is no instantaneous transfer of information due to these correlations between the two particles. The apparatus of relativistic quantum theory was initially constructed in such a way that events located in space-time on opposite sides of the light cone cannot influence each other. Simply put, no signal, no influence or disturbance can travel faster than light. Both particles are actually states of the same field, for example, electron-positron. By influencing the field at one point (particle 1), we create a disturbance that propagates like waves on water. In non-relativistic quantum mechanics, the speed of light is considered infinitely large, which gives rise to the illusion of instantaneous change.

The situation when particles separated by large distances remain bound in pairs seems paradoxical due to classical ideas about particles. We must remember that it is not particles that really exist, but fields. What we think of as particles are simply states of these fields. The classical idea of ​​particles is completely unsuitable in the microworld. Questions immediately arise about the size, shape, material and structure of elementary particles. In fact, situations that are paradoxical for classical thinking also arise with one particle. For example, in the Stern-Gerlach experiment, a hydrogen atom flies through a non-uniform magnetic field directed perpendicular to the speed. The nuclear spin can be neglected due to the smallness of the nuclear magneton, even if the electron spin is initially directed along the velocity.

The evolution of the wave function of an atom is not difficult to calculate. The initial localized wave packet splits into two identical ones, flying symmetrically at an angle to the original direction. That is, an atom, a heavy particle, usually considered as classical with a classical trajectory, split into two wave packets that can fly apart over quite macroscopic distances. At the same time, I will note that from the calculation it follows that even the ideal Stern-Gerlach experiment is not able to measure the spin of a particle.

If the detector binds a hydrogen atom, for example, chemically, then the “halves” - two scattered wave packets - are collected into one. How such localization of a smeared particle occurs is a separate theory that I do not understand. Those interested can find extensive literature on this issue.

Conclusion

The question arises: what is the meaning of numerous experiments demonstrating correlations between particles at large distances? In addition to confirming quantum mechanics, which no normal physicist has long doubted, this is a spectacular demonstration that impresses the public and amateur officials who allocate funds for science (for example, the development of quantum communication lines is sponsored by Gazprombank). For physics, these expensive demonstrations do not yield anything, although they allow the development of experimental techniques.

Literature
1. Landau, L. D., Lifshits, E. M. Quantum mechanics (non-relativistic theory). - 3rd edition, revised and expanded. - M.: Nauka, 1974. - 752 p. - (“Theoretical Physics”, Volume III).
2. Eberhard, P.H., “Bell’s theorem and the different concepts of nonlocality,” Nuovo Cimento 46B, 392-419 (1978)

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• Translation

Quantum entanglement is one of the most complex concepts in science, but its basic principles are simple. And once understood, entanglement opens the way to a better understanding of concepts such as the many worlds in quantum theory.

An enchanting aura of mystery surrounds the concept of quantum entanglement, as well as (somehow) the related requirement of quantum theory that there must be “many worlds.” And yet, at their core, these are scientific ideas with down-to-earth meaning and specific applications. I would like to explain the concepts of entanglement and many worlds as simply and clearly as I know them.

I

Entanglement is thought to be a phenomenon unique to quantum mechanics—but it is not. In fact, it may be more understandable to begin with (although this is an unusual approach) to consider a simple, non-quantum (classical) version of entanglement. This will allow us to separate the subtleties associated with entanglement itself from other oddities of quantum theory.

Entanglement occurs in situations in which we have partial information about the state of two systems. For example, two objects can become our systems – let’s call them kaons. "K" will stand for "classical" objects. But if you really want to imagine something concrete and pleasant, imagine that these are cakes.

Our kaons will have two shapes, square or round, and these shapes will indicate their possible states. Then the four possible joint states of the two kaons will be: (square, square), (square, circle), (circle, square), (circle, circle). The table shows the probability of the system being in one of the four listed states.

We will say that kaons are “independent” if knowledge about the state of one of them does not give us information about the state of the other. And this table has such a property. If the first kaon (cake) is square, we still don't know the shape of the second one. Conversely, the form of the second tells us nothing about the form of the first.

On the other hand, we will say that two kaons are entangled if information about one of them improves our knowledge about the other. The second tablet will show us strong confusion. In this case, if the first kaon is round, we will know that the second one is also round. And if the first kaon is square, then the second one will be the same. Knowing the shape of one, we can unambiguously determine the shape of the other.

The quantum version of entanglement looks essentially the same - it is a lack of independence. In quantum theory, states are described by mathematical objects called wave functions. The rules that combine wave functions with physical possibilities give rise to very interesting complications that we will discuss later, but the basic concept of entangled knowledge that we demonstrated for the classical case remains the same.

Although brownies cannot be considered quantum systems, entanglement in quantum systems occurs naturally, such as after particle collisions. In practice, unentangled (independent) states can be considered rare exceptions, since correlations arise between them when systems interact.

Consider, for example, molecules. They consist of subsystems - specifically, electrons and nuclei. The minimum energy state of a molecule, in which it usually exists, is a highly entangled state of electrons and nucleus, since the arrangement of these constituent particles will not be independent in any way. When the nucleus moves, the electron moves with it.

Let's return to our example. If we write Φ■, Φ● as wave functions describing system 1 in its square or round states and ψ■, ψ● for wave functions describing system 2 in its square or round states, then in our working example all states can be described , How:

Independent: Φ■ ψ■ + Φ■ ψ● + Φ● ψ■ + Φ● ψ●

Entangled: Φ■ ψ■ + Φ● ψ●

The independent version can also be written as:

(Φ■ + Φ●)(ψ■ + ψ●)

Note how in the latter case the brackets clearly separate the first and second systems into independent parts.

There are many ways to create entangled states. One is to measure a composite system that gives you partial information. One can learn, for example, that two systems have agreed to be of the same form without knowing which form they have chosen. This concept will become important a little later.

The more common effects of quantum entanglement, such as the Einstein-Podolsky-Rosen (EPR) and Greenberg-Horn-Seilinger (GHZ) effects, arise from its interaction with another property of quantum theory called the complementarity principle. To discuss EPR and GHZ, let me first introduce this principle to you.

Up to this point, we have imagined that kaons come in two shapes (square and round). Now let’s imagine that they also come in two colors – red and blue. Considering classical systems such as cakes, this additional property would mean that the kaon could exist in one of four possible states: red square, red circle, blue square, and blue circle.

But quantum cakes are quantons... Or quantons... They behave completely differently. The fact that a quanton in some situations may have different shapes and colors does not necessarily mean that it simultaneously has both shape and color. In fact, the common sense that Einstein demanded of physical reality does not correspond to experimental facts, as we will soon see.

We can measure the shape of a quanton, but in doing so we will lose all information about its color. Or we can measure the color but lose information about its shape. According to quantum theory, we cannot measure both shape and color at the same time. No one's view of quantum reality is complete; we have to take into account many different and mutually exclusive pictures, each of which has its own incomplete picture of what is happening. This is the essence of the principle of complementarity, as formulated by Niels Bohr.

As a result, quantum theory forces us to be careful in attributing properties to physical reality. To avoid contradictions, we must admit that:

A property does not exist unless it is measured.
Measurement is an active process that changes the system being measured

II

Now we will describe two exemplary, but not classical, illustrations of the oddities of quantum theory. Both have been tested in rigorous experiments (in real experiments, people measure not the shapes and colors of cakes, but the angular momenta of electrons).

Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) described a surprising effect that occurs when two quantum systems become entangled. The EPR effect combines a special, experimentally achievable form of quantum entanglement with the principle of complementarity.

An EPR pair consists of two quantons, each of which can be measured in shape or color (but not both at once). Suppose we have many such pairs, all of them the same, and we can choose what measurements we make on their components. If we measure the shape of one of the members of an EPR pair, we are equally likely to get a square or a circle. If we measure color, we are equally likely to get red or blue.

Interesting effects that seemed paradoxical to EPR arise when we measure both members of the pair. When we measure the color of both members, or their shape, we find that the results are always the same. That is, if we discover that one of them is red and then measure the color of the second, we also discover that it is red - and so on. On the other hand, if we measure the shape of one and the color of the other, no correlation is observed. That is, if the first one was a square, then the second one could be blue or red with equal probability.

According to quantum theory, we will obtain such results even if the two systems are separated by a huge distance and the measurements are carried out almost simultaneously. The choice of measurement type at one location appears to affect the state of the system at another location. This “frightening action at a distance,” as Einstein called it, apparently requires the transmission of information—in our case, information about a measurement being made—faster than the speed of light.

But is it? Until I know what results you got, I don't know what to expect. I get useful information when I know your result, not when you take a measurement. And any message containing the result you receive must be transmitted in some physical way, slower than the speed of light.

With further study, the paradox collapses even more. Let's consider the state of the second system if the measurement of the first gave a red color. If we decide to measure the color of the second quanton, we get red. But by the principle of complementarity, if we decide to measure its shape when it is in the "red" state, we have an equal chance of getting a square or a circle. Therefore, the result of EPR is logically predetermined. This is simply a restatement of the principle of complementarity.

There is no paradox in the fact that distant events are correlated. After all, if we put one of two gloves from a pair into boxes and send them to different ends of the planet, it is not surprising that by looking in one box, I can determine which hand the other glove is intended for. Likewise, in all cases, the correlation of EPR pairs must be recorded on them when they are nearby so that they can withstand subsequent separation, as if having memory. The strangeness of the EPR paradox is not in the possibility of correlation itself, but in the possibility of its preservation in the form of additions.

III

Daniel Greenberger, Michael Horn and Anton Zeilinger discovered another beautiful example of quantum entanglement. IT includes three of our quantons, which are in a specially prepared entangled state (GHZ-state). We distribute each of them to different remote experimenters. Each of them chooses, independently and randomly, whether to measure color or shape and records the result. The experiment is repeated many times, but always with three quantons in the GHZ state.

Each individual experimenter obtains random results. Measuring the shape of a quanton, he obtains with equal probability a square or a circle; when measuring the color of a quanton, it is equally likely to be red or blue. So far everything is ordinary.

But when experimenters get together and compare the results, the analysis shows a surprising result. Let's say we call the square shape and red color “good”, and the circles and blue color “evil”. Experimenters find that if two of them decide to measure shape and the third decides to measure color, then either 0 or 2 of the measurements are “evil” (i.e., round or blue). But if all three decide to measure a color, then either 1 or 3 dimensions are evil. This is what quantum mechanics predicts, and this is exactly what happens.

Question: Is the amount of evil even or odd? Both possibilities are realized in different dimensions. We have to abandon this issue. It makes no sense to talk about the amount of evil in a system without relating it to how it is measured. And this leads to contradictions.

The GHZ effect, as physicist Sidney Coleman describes it, is “a slap in the face from quantum mechanics.” It breaks down the conventional, experiential expectation that physical systems have predetermined properties independent of their measurement. If this were so, then the balance of good and evil would not depend on the choice of measurement types. Once you accept the existence of the GHZ effect, you will not forget it, and your horizons will be expanded.

IV

For now, we are discussing how entanglement prevents us from assigning unique independent states to multiple quantons. The same reasoning applies to changes in one quanton that occur over time.

We talk about “entangled histories” when it is impossible for a system to be assigned a certain state at each moment in time. Just as in traditional entanglement we rule out possibilities, we can create entangled histories by making measurements that collect partial information about past events. In the simplest entangled stories we have one quanton that we study at two different points in time. We can imagine a situation where we determine that the shape of our quanton was square both times, or round both times, but both situations remain possible. This is a temporal quantum analogy to the simplest versions of entanglement described earlier.

Using a more complex protocol, we can add a little extra detail to this system, and describe situations that trigger the "many-worlds" property of quantum theory. Our quanton can be prepared in the red state, and then measured and obtained in blue. And as in the previous examples, we cannot permanently assign a quanton the property of color in the interval between two dimensions; It does not have a specific form. Such stories realize, in a limited but completely controlled and precise way, the intuition inherent in the many-worlds picture of quantum mechanics. A certain state can be divided into two contradictory historical trajectories, which then connect again.

Erwin Schrödinger, the founder of quantum theory, who was skeptical about its correctness, emphasized that the evolution of quantum systems naturally leads to states, the measurement of which can give extremely different results. His thought experiment with "Schrodinger's cat" postulates, as we know, quantum uncertainty, taken to the level of influence on feline mortality. Before measuring, it is impossible to assign the property of life (or death) to a cat. Both, or neither, exist together in an otherworldly world of possibility.

Everyday language is ill-suited to explain quantum complementarity, in part because everyday experience does not include it. Practical cats interact with surrounding air molecules, and other objects, in completely different ways, depending on whether they are alive or dead, so in practice the measurement takes place automatically, and the cat continues to live (or not live). But the stories describe the quantons, which are Schrödinger's kittens, with confusion. Their full description requires that we consider two mutually exclusive trajectories of properties.

Controlled experimental implementation of entangled stories is a delicate thing, since it requires the collection of partial information about quantons. Conventional quantum measurements typically collect all the information at once—determining an exact shape or a precise color, for example—rather than obtaining partial information several times. But it can be done, albeit with extreme technical difficulties. In this way we can assign a certain mathematical and experimental meaning to the extension of the concept of “many worlds” in quantum theory, and demonstrate its reality.

Quantum entanglement, or “spooky action at a distance” as Albert Einstein called it, is a quantum mechanical phenomenon in which the quantum states of two or more objects are interdependent. This dependence persists even if the objects are many kilometers away from each other. For example, you can entangle a pair of photons, take one of them to another galaxy, and then measure the spin of the second photon - and it will be opposite to the spin of the first photon, and vice versa. They are trying to adapt quantum entanglement for instant transmission of data over gigantic distances or even for teleportation.

Physicists from the Scottish University of Glasgow reported an experiment in which scientists were able to obtain the first ever photograph of particles. A phenomenon so strange by physics standards that even a great 20th century scientist nicknamed it “spooky action at a distance.” The achievement of Scottish scientists is very important for the development of new technologies. Why? Let's figure it out.

We have already written more than once that quantum communication devices are being tested every now and then in different parts of the world. It would seem that all this will not go beyond experiments soon, but, as the Xinhua news agency reports, China has completed the creation of the country's first commercial ultra-secure quantum communication network. Commissioning is planned in the very near future.

Quantum entanglement (entanglement) is that two entangled particles, after being separated into different regions of space, retain some semblance of an information connection with each other. By making a measurement on one particle, we at the same moment, instantly determine the state of another particle, no matter how far these particles are from each other. From the point of view of the formalism of quantum mechanics, these results are impeccable, but this strictly contradicts common sense, since during the measurement these two particles no longer interact and any operations on the first particle cannot affect the state of the second particle.

The most famous example of quantum entanglement is the so-called EPR paradox (Einstein, Podolsky and Rosen) - two connected photons in the process of separation (flying apart) retain such a semblance of information connection. In this case, the quantum state of one photon, for example, polarization, can be instantly transferred to another photon, which in this case becomes an analogue of the first and vice versa. Consider photon 1. Having an undefined polarization before measurement, photon 1 receives polarization during its measurement. Photon 2, which did not have a specific polarization, is projected into a state of polarization parallel to the measurement result on photon 1. This is very surprising because this change in the description of photon 2 occurs instantly, regardless of the distance between the photons at the time of the first measurement. This picture, called “nonlocality,” is in conflict with STR, although there is no transfer of real information from one photon to another. Therefore, the transmitted (conditional) information between EPR particles is sometimes called “quantum information”.

In 2008, a group of Swiss researchers from the University of Geneva managed to spread two streams of entangled photons over a distance of 18 kilometers. Among other things, this made it possible to make time measurements with previously unattainable accuracy. As a result, it was found that if some kind of hidden interaction occurs, then the speed of its propagation must be at least 100,000 times higher than the speed of light in a vacuum. At lower speeds, time delays would be noticed.

P.S. If you read the entire text and do not understand, do not be discouraged. This means that with common sense you are OK.

I slightly disagree with the previous speaker regarding the philosophical side of the issue, interpretation. Quantum entanglement is not exactly a connection, much less instantaneous. And in quantum theory there is no non-locality and contradictions with SRT; moreover, it is built on SRT. All the oddities of quantum mechanics arise when trying to move from the quantum picture of the world to the classical one, that is, where “measurement” takes place. This is an obvious flaw in the Copenhagen interpretation, which real physicists, as a rule, simply do not pay attention to, because they do not need to chatter about the nature of things, but calculate the result of the experiment, and this is the correct approach. But nevertheless, in reality everything is a little different from what it really is.

This is rather analogous to the situation with shoes - if I have a left one, then I instantly recognize that you have a right one. This is not due to a "real" but a logical connection between the shoes. Therefore, locality does not need to be violated in order to implement this connection. But! In quantum mechanics this happens much more cunningly, because the logic there is different. Because measurement itself is also quantum entanglement! That is, a logical connection arises not only between the shoes, but also the states of the experimenter who “measured” them. The left shoe is now associated with the state "I know I have a left shoe." And since the left one was logically connected to the right one, I now know that the second shoe is the right one. This is ordinary logic, only in quantum mechanics the system can be in some mixture (superposition) of states (left/right + right/left), and after the “measurement” you yourself find yourself in a superposition (my right, my neighbor’s left + vice versa). Which also contradicts common sense, but is perfectly friendly with locality, causality, unitarity, and other principles on which physics stands.

Launched last year, the Chinese satellite Micius successfully completed orbital tests and set a new record for quantum communications. It generated a pair of entangled photons, separated them and transmitted them simultaneously to two ground stations located 1203 km apart. Ground stations then used the quantum teleportation effect to exchange encrypted messages. Potentially, the launch of such satellites opens up the possibility of creating global communication systems protected from interception at the level of physical principles. The experiment has already been dubbed “the beginning of the quantum Internet.”

The device, costing about $100 million, was created as part of the QUESS (Quantum Science Satellite) project, a joint initiative of the Chinese and Austrian Academy of Sciences. “This project is intended to prove the possibility of introducing quantum communications on a global scale,” comments Anton Zeilinger, an expert in quantum physics at the University of Vienna, who was the first in the world to perform quantum teleportation of states of entangled photons.

Teleportation quantum and fantastic

The term "teleportation" can be misleading. In quantum systems, it means the transfer of information between pre-generated pairs of linked particles, that is, characterized by a common wave function. In this case, no transfer of matter or energy occurs, and general relativity is not violated. The essence of quantum teleportation is to use the interconnected quantum states of entangled particles to encode and instantly transmit information. Measuring (that is, changing) the properties of one particle will instantly change the properties of the second, no matter what distance they are located.

The satellite, weighing more than 600 kg, was launched into a sun-synchronous orbit at an altitude of 494.8–511.1 km using the Long March 2D launch vehicle (also known as the Long March, or “Long March”) launched from the Jiuquan Satellite Launch Center 16 August 2016. After many months of testing, it was transferred to the Chinese Academy of Sciences.

The orbital parameters were chosen so that the satellite appeared in the same place every night. Ground stations tracked the satellite and established optical communication links with it to receive single entangled photons. The satellite was monitored by three optical telescopes in Deling, Lijiang and Nanshan. The satellite managed to establish communication with all three ground stations.

According to the plan, Micius will become the first device in the global quantum communication network, which China intends to create by 2030. One of the tasks of his scientific mission is the quantum transmission of information via a communications channel protected from interception between Beijing and Vienna. For this purpose, the satellite is equipped with experimental equipment: an emitter of pairs of entangled photons and a high-speed coherent laser transmitter.

By the way, the satellite Micius (in another transcription - Mozi) is named after the ancient Chinese philosopher Mo Tzu. According to the leading specialist in the development of Micius, academician Jian-Wei Pan from the University of Science and Technology of China, his compatriot Mo Tzu described the nature of the propagation of light even before our era, which gave rise to the development of optical communications. Let’s leave national claims to primacy in optics outside the scope of this article and look at what makes the record so interesting, and at the same time try to understand the basics of quantum communications.

Sino-Austrian Agreement

It was no coincidence that Austria became a participant in the project: it was a group of physicists from the Austrian University of Innsbruck in 1997 that first managed to demonstrate quantum teleportation of states in a pair of entangled photons.

Modern China also has an interesting history of developing quantum communications. In 2005, scientists from the University of Science and Technology of China were able to transmit the quantum state of entangled particles over 7 km in open air. Later, using custom-made optical fiber, this distance was increased to 400 km. For the first time, the transmission of entangled photons through the atmosphere and over a considerable distance was also accomplished by physicists from the University of Science and Technology of China and Beijing Tsinghua University. In May 2010, they successfully transmitted a pair of entangled photons over 16 km (see Nature Photonics).

Fiber optic or line-of-sight communications are needed only for the initial separation of entangled photons. Subsequently, information about changes in their quantum state is transmitted instantly and regardless of distance. Therefore, in addition to the traditionally listed advantages of quantum data transmission (high coding density, speed and security from interception), Zeilinger notes another important property: quantum teleportation is also possible in the case when the exact relative position of the receiver and transmitter is unknown. This is especially important for satellite communication systems, since the relative positions of network nodes in them are constantly changing.

In a new experiment using Micius, laboratories located in the capitals of China and Austria transmitted a message encrypted with the Vernam cipher to each other over open terrestrial channels. The results of measuring the quantum properties of pairs of entangled photons received from the satellite were used as a cryptographic key.

Obviously, receiving billions of photons on Earth even from the distant Sun is not a problem. Anyone can do this on a sunny day by simply stepping out of the shade. To simultaneously detect a certain pair of entangled photons from a satellite in two different laboratories and measure their quantum properties is an extremely difficult technical task. To solve this problem, the QUESS project used adaptive optics. It constantly measures the degree of distortion caused by turbulence in the Earth's atmosphere and compensates for it. Additionally, optical filters were used to cut off moonlight and urban illumination. Without them, there was too much noise in the optical communication line.

Each satellite pass over Chinese territory lasted only 275 seconds. During this time, it was necessary to simultaneously install two outgoing channels from it. In the first series of experiments - between Delinga and Nanshan (distance 1120 km). In the second - between Delinga and Lijian (1203 km). In both experiments, pairs of entangled photons were successfully received from the satellite and the secure communication channel was operational.

This is considered a breakthrough for several reasons. First, Micius was the first successful experiment in satellite quantum communications. Until now, all such experiments were carried out in ground-based laboratories, where the receiver and transmitter were located at much shorter distances from each other. Secondly, other experiments required the use of some kind of isolated medium to transmit entangled photons. For example, fiber optic communication lines. Third, in quantum communications, single photons are transmitted and detected over an optical fiber, and the satellite increases the effective exchange rate.

Quantum communications in Russia

Since 2014, a project in the field of terrestrial quantum communications has been launched in Russia. Investments in it exceed 450 million rubles, but the practical output is still very modest. On May 31, 2016, employees of the Russian Quantum Center launched the first domestic quantum communication line. Created on the basis of the existing fiber-optic network, it connected two Gazprombank branches in Moscow - on Koroviy Val and in Novye Cheryomushki. The distance between these buildings is about 30 km. For now, the Russian quantum communication line functions as an experimental one.

The signal from Micius traveled through the atmosphere and was simultaneously received by two ground stations. “If we used 1,200 km of optical fiber to distribute pairs of entangled photons on Earth, then due to the loss of signal power with distance, we could transmit only one pair per second. The satellite helps overcome this barrier. We have already improved the distribution speed by 12 orders of magnitude compared to previous technologies,” says Jian-Wei Pan.

Quantum data transmission via satellite opens up the possibility of building global communication systems that are maximally protected from interception at the level of physical principles. “This is the first step towards worldwide secure quantum communication and perhaps even a quantum Internet,” says Anton Zeilinger.

The paradox of this achievement is that even the authors of the project do not know all the details about the operation of the quantum communication system. There are only working hypotheses, their experimental testing and long debates about the correct interpretation of the results obtained. This often happens: first a phenomenon is discovered, then it is actively used, and only after a long time is someone able to understand its essence found. Primitive people knew how to make fire, but none of them understood the physical and chemical processes of combustion. We had to understand them in order to make a quality transition from a fire to an internal combustion engine and a rocket engine.

Quantum teleportation is a completely confusing thing in every sense. Let's try to abstract from complex formulas and invisible concepts and understand its basics. Old acquaintances will help us with this - interlocutors Alice, Bob and Malory, who is always eavesdropping on them.

How Alice and Bob circled Mallory

In a conventional communication system, Malory is assigned the role of "man in the middle." He imperceptibly wedges himself into the transmission line, intercepts the message from Alice, reads it, if desired, also changes it and passes it on to Bob. Naive Bob suspects nothing. So Malory takes his answer, does whatever she wants with it, and sends it to Alice. This is how all correspondence, telephone conversations and any other classical type of communication are compromised. With quantum communication this is impossible in principle. Why?

To create a cryptographic key there, Alice and Bob first use a series of measurements on pairs of entangled photons. The results of these measurements then become the key to encrypt and decrypt messages sent over any open channel. If Malory intercepts the entangled photons, he will destroy the quantum system and both interlocutors will immediately know about it. Malory would physically be unable to retransmit the same photons because it would violate a principle of quantum mechanics known as the “no cloning rule.”

This happens because the properties of the macro- and microworld are radically different. Any macro object always exists in a very specific state. Here is a piece of paper, it is lying there. Here it was placed in an envelope and sent by airmail. We can measure any parameter of a paper message at any time, and this will not affect its essence in any way. It will not change its content due to weighing or X-raying and will not fly faster in the radar beam with which we measure the speed of the aircraft.

This is not the case for elementary particles. They are described as probabilistic states of a quantum system, and any measurement transfers it to a strictly defined state, that is, changes it. The very influence of measurement on the result does not fit well into the usual worldview. However, from a practical point of view, it is interesting because the state of the transmitted quantum system cannot be secretly known. An attempt to intercept and read such a message will simply destroy it. Therefore, it is believed that quantum communication completely eliminates the possibility of a MitM attack.

Any elementary particles are theoretically suitable for quantum data transfer. Previously, experiments were carried out with electrons, protons and even ions of various metals. In practice, for now it is most convenient to use photons. They are easy to emit and register. There are already ready-made devices, protocols and entire fiber-optic networks for traditional data transmission. The difference between quantum communication systems is that pairs of previously entangled photons must be transmitted to them.

How not to get confused in two photons

The entanglement of elementary particles gives rise to heated debates around the principle of locality - the postulate that only objects sufficiently close to each other participate in interactions. All experimental tests in classical mechanics are based on this principle. The result of any experiment in it depends only on the directly interacting bodies and can be accurately calculated in advance. The number of observers will also not affect it in any way. In the case of quantum mechanics there is no such certainty. For example, it is impossible to say in advance what the polarization of one of the entangled photons will be.

Einstein cautiously suggested that the probabilistic nature of the predictions of quantum mechanics is explained by the presence of some hidden parameters, that is, a banal incompleteness of the description. Thirty years later, Bell responded by creating a series of inequalities that could theoretically confirm the presence of hidden parameters in experiments with quantum particles by analyzing the probability distribution in a series of experiments. Alain Aspe, and then other experimenters, demonstrated the violation of Bell's inequalities.

In 2003, theoretical physicist from the University of Illinois Tony Leggett summarized the accumulated data and proposed completely abandoning the principle of locality in any reasoning about quantum systems. Later, a group of scientists from the Zurich Institute for Theoretical Physics and the Institute of Applied Physics at the Technical University of Darmstadt, led by Roger Kohlbeck, came to the conclusion that the Heisenberg principle is also incorrect for entangled elementary particles.

This constant rethinking of quantum mechanics occurs because we are trying to think in familiar terms in an unfamiliar environment. The entangled states of particles and, in particular, photons are not at all a mystical property. It does not violate, but rather complements, the known laws of physics. It’s just that physicists themselves cannot yet describe the observed effects in a consistent theory.

Quantum entanglement has been observed in experiments since the 1970s. Pairs of pre-entangled particles separated at any distance instantly (that is, faster than the speed of light) change each other’s properties - hence the term “teleportation”. For example, if you change the polarization of one photon, its pair will immediately change its own. Miracle? Yes, if you don’t remember that initially these photons were a single whole, and after separation their polarization and other properties also turned out to be interconnected.

Surely you remember about the duplicity of the photon: it interacts like a particle, but propagates like a wave. There are different techniques for creating a pair of entangled photons, one of which is based on wave properties. It generates one photon with a shorter wavelength (for example, 512 nm), and then it is divided into two photons with a longer wavelength (1024 nm). The wavelength (frequency) of such photons is the same, and all quantum properties of the pair are described by a probabilistic model. “Change” in the microcosm means “measure”, and vice versa.

A photon-particle has quantum numbers - for example, helicity (positive or negative). A photon-wave has a polarization - for example, horizontal or vertical (or left and right circular - depending on which plane and direction of movement we are considering).

What these properties will be for each photon from a pair is not known in advance (see the probabilistic principles of quantum mechanics). But in the case of entangled photons, we can say that they will be the opposite. Therefore, if you change (measure) the characteristics of one photon from a pair, they will instantly become determined for the second, even if it is located 100500 parsecs away. It is important to understand that this is not simply removing the unknown. This is precisely a change in the quantum properties of particles as a result of the transition from a probabilistic state to a deterministic one.

The main technical challenge is not creating entangled pairs of photons. Almost any light source produces them constantly. Even the light bulb in your room emits millions of entangled photons. However, it can hardly be called a quantum device, since in such chaos the quantum entanglement of the born pairs quickly disappears, and countless interactions prevent the efficient transfer of information.

Experiments with quantum entanglement of photons usually use the properties of nonlinear optics. For example, if you shine a laser on a piece of lithium niobate or other nonlinear crystal cut in a certain way, then pairs of photons with mutually orthogonal (that is, horizontal and vertical) polarization will appear. One (ultra)short laser pulse is strictly one pair of photons. That's where the magic is!

Additional bonus of quantum data transfer

Helicity, polarization are all additional ways to encode a signal, so more than one bit of information can be transmitted with one photon. This is how quantum communication systems increase data transmission density and speed.

Using quantum teleportation to transmit information is still too difficult, but progress in this area is moving rapidly. The first successful experience was registered in 2003. Zeilinger's group performed the transfer of quantum states of entangled particles separated by 600 m. In 2010, Jian-Wei Pan's group increased this distance to 13 km, and then in 2012 broke their own record, recording successful quantum teleportation at a distance of 97 km. In the same 2012, Zeilinger took revenge and increased the distance to 143 km. Now, through joint efforts, they have made a real breakthrough - they have completed a transmission of 1203 km.