Quantum computers, quantum cryptography and the quantum (here insert the name) are often in the news these days. The articles about them inevitably refer to *tangling*, a property of quantum physics that makes all these magical devices possible.

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Einstein calls the ghostly "spooky action from a distance" – a name that has remained and is becoming more and more popular. In addition to building better quantum computers, understanding and mastery of tangling is also beneficial in other ways.

For example, it can be used for more accurate gravitational wave measurements and a better understanding of the properties of exotic materials. It also occurs elsewhere: I study how atoms struggle with each other to understand how this affects the accuracy of atomic clocks.

But what *it is* tangling? Is there any way to understand this "spooky" phenomenon? I will try to explain it by compiling two concepts of physics: conservation laws and quantum superpositions.

## Conservation laws

Conservation laws are some of the deepest and most common in physics. The Law on Energy Conservation states that the total amount of energy in an isolated system remains fixed (although it can be converted from electrical to mechanical to heat, etc.). This law is the basis for the operation of all our machines, whether they are steam engines or electric cars. Nature conservation laws are a kind of accounting: you can exchange parts of energy around, but the total amount must remain the same.

Maintaining inertia (mass, speed and speed) is the reason why, when two ice slides with different masses separate from one another, the lighter moves faster than the heavier. This law is also the basis of the famous statement that "every action has the same and opposite reaction" *angular* Inertia is why – let's go back to ice skaters – a spinning figure can rotate faster by moving his hands to his body.

These conservation laws are experimentally tested to work on an extraordinary range of rocks in the universe, from black holes in distant galaxies to the smallest rotating electrons.

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## Quantum supplement

Imagine yourself a good march through the woods. You come to a branch in the path, but you are a struggle to decide whether to go left or right. The road to the left looks dark and gloomy, but it is believed to lead to some pretty views while on the right it looks sunny but steep. Finally, you decide to go right, thinking thoughtfully about the path that has not been taken. In the quantum world you could choose both.

For the systems described by quantum mechanics (ie things that are sufficiently isolated from heat and external interference), the rules are more interesting. Like a rotating rotating part, the electron can, for example, be in a state in which it rotates clockwise or in another state where it rotates counterclockwise. Unlike the rotating tip, it can also be in a condition that is so *[clockwise spinning] + [anticlockwise spinning]*,

*The states of the quantum systems can be assembled and subtracted from one another*, Mathematically, the rules for combining quantum states can be described in the same way as the rules for adding and subtracting vectors. The word for such a combination of quantum states is a *superposition*This is really what is behind the strange quantum effects you may have heard of, such as the double-gap experiment or the double-wavelength duality.

Say you decide to force an electron in *[clockwise spinning] + [anticlockwise spinning]* superposition status to give a definite answer. Then the electron accidentally ends or in *[clockwise spinning]* or in. t *[anticlockwise spinning]* condition. The coefficient of one score relative to the other is easy to calculate (with a good book on physics in hand). The inherent chance of this process can disturb you if your worldview requires the universe to behave in a fully predictable way but … *that's at* (experimentally tested) *rival*,

## Conservation laws and quantum mechanics

Let us now put these two ideas together and apply the law of energy conservation to a pair of quantum particles.

Imagine a pair of quantum particles (for example, atoms) that start with a total of 100 energy units. You and your friend divide the couple by taking one. You find that yours has 40 energy units. By using the energy conservation law, you can conclude that the one your friend needs to have 60 energy units. As soon as you understand the energy of your atom, you immediately know the energy of your friend's atom. You will know this even if your friend never gives you any information. And you will know this even if your friend was on the other side of the galaxy during the measurement of your atom's energy. Nothing scary about this (once you realize that this is just a correlation, not a causal link).

But the quantum states of a pair of atoms may be more interesting. The pair's energy can be divided into many possible ways (according to energy saving, of course). The combined state of the pair of atoms may be in a superposition, for example:

[your atom: 60 units; friend’s atom: 40 units] + [your atom: 70 units; friend’s atom: 30 units],

It is *tangled state* of the two atoms. Neither your atom nor your friend has a certain energy in this superposition. Nevertheless, the properties of the two atoms are correlated due to the conservation of energy: their energies always add up to 100 units.

For example, if you measure your atom and find it in a state of 70 energy, you can be sure your friend's atom has 30 energy units. You will know this even if your friend never gives you any information. And thanks to the preservation of energy, you will know this even if your friend was on the other side of the galaxy.

Nothing scary about that.

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