# The imaginary part of quantum mechanics really does exist

It was commonly assumed that** complex numbers**, ie those that contain an imaginary number component and (i squared results in minus one) are just a mathematical trick. However, a Polish-Sino-Canadian team of scientists has proven that the imaginary part of the **quantum mechanics** can be seen in action in the real world - reports the Center for New Technologies at the University of Warsaw.

Our intuitive ideas about the ability of numbers to describe the physical world require significant revision. Up until now it seemed that only real numbers were associated with measurable physical quantities. However, it has succeeded **Quantum states** from **entangled photons** to find that cannot be distinguished without resorting to complex numbers. In addition, the researchers conducted an experiment that determined the meaning of complex numbers for the **quantum mechanics** approved

*Image source: Pixabay*

The research was carried out by the team of Dr. Alexander Streltsov from the Center for Quantum Optical Technologies (QOT) at the University of Warsaw with the participation of scientists from the University of Science and Technology of China (USTC) in Hefei and the University of Calgary (UCalgary). Articles describing the theory and measurements are in Physical Review Letters and Physical Review A appeared.

In physics, complex numbers were considered to be of a purely mathematical nature. Although they play a fundamental role in the equations of the **quantum mechanics** play, they were just treated as a tool, something that makes physicists' calculations easier. We have theoretically and experimentally proven that there are **Quantum states** there that only under the indispensable participation of** complex numbers** can be differentiated, "comments Dr. Streltsov.

Compound numbers are made up of two components, real and imaginary. They are of the form a + bi, where a and b are real. The bi-component is responsible for the specific properties of the complex numbers. The key role is played by the imaginary number i. The number i is the square root of -1 (so if we were to square it we would get minus one).

In the physical world, it is difficult to imagine anything that could be directly related to the number i. There can be 2 or 3 apples on the table, this is normal. If we take away an apple, we can speak of a physical defect and describe it by the negative integer -1. We can cut the apple in two or three parts and thus get physical equivalents of the measurable numbers 1/2 or 1/3. If the table were a perfect square, its diagonal (the unmeasurable) square root of the number 2 would be longer than its side. At the same time, despite the most sincere intentions, it is impossible to put apples in the number i on the table.

The surprising career of complex numbers in physics is related to the fact that with their help all kinds of **vibrations** Can be described much more conveniently than with the common trigonometric functions. The calculations are therefore carried out with composite numbers and in the end only the real numbers that occur in them are taken into account.

Compared to other physical theories, the **quantum mechanics** something special because it has to describe objects that can behave as particles under certain conditions and as waves under others. The basic equation of this theory, which is accepted as a postulate, is the Schrödinger equation. It describes the changes over time of a certain function, the so-called wave function, which occurs with the **Probability distribution**to find the system in this or that state is related. In the **Schrödinger equation** however, there is an explicit imaginary number i right next to the wave function.

For decades there has been a debate about whether or not to be consistent and complete **quantum mechanics** can be generated with real numbers alone. That's why we decided **Quantum states** that can only be distinguished from one another with complex numbers. The crucial moment was an experiment in which we created these states and physically checked whether they were distinguishable or not, "says Dr. Streltsov, whose research was funded by the Polish Science Foundation.

The experiment that played the role of **complex numbers in quantum mechanics** verified, can be represented in the form of a game between Alice and Bob with the participation of the game master. Using a device with lasers and crystals, the game master binds two photons into one of two **Quantum states**whose distinction necessarily requires the use of complex numbers. He then sends a **Photon** to Alice and the other to Bob. They each measure their photon and then communicate with the other to determine the existing correlations.

Assume that Alice and Bob's measurements can only take the values 0 or 1. Alice sees a meaningless sequence of zeros and ones, like Bob. However, when they communicate, they can make connections between the corresponding measurements. If the GM has sent you a correlated state, if one sees the result 0, the other will too. If you have one **anticorrelated state** received, Alice measures 0, for Bob it will be 1. With mutual consent, Alice and Bob could distinguish our states, but only if theirs **Quantum nature** is fundamentally complex, says Dr. Streltsov.

For the theoretical description, an approach was used which is called **Quantum resource theory** is known. The experiment itself with local differentiation from entangled **Two-photon states** was carried out in a laboratory in Hefei using linear optics techniques. The quantum states prepared by the researchers turned out to be distinguishable, which proves that complex numbers are an integral, indistinguishable part of quantum mechanics.

The achievement of the Polish-Sino-Canadian research team is fundamental, but so profound that it can be translated into new **Quantum technologies** could knock down. In particular, exploring the role of complex numbers in the **quantum mechanics** can help increase the sources of efficiency **Quantum computers** To better understand qualitatively new calculating machines that can solve certain problems at speeds unattainable for classic computers, the announcement said.