(Press-News.org) For almost a century, physicists have been intrigued by the fundamental question: why are complex numbers so important in quantum mechanics, that is, numbers containing a component with the imaginary number i? Usually, it was assumed that they are only a mathematical trick to facilitate the description of phenomena, and only results expressed in real numbers have a physical meaning. However, a Polish-Chinese-Canadian team of researchers has proved that the imaginary part of quantum mechanics can be observed in action in the real world.
We need to significantly reconstruct our naive ideas about the ability of numbers to describe the physical world. Until now, it seemed that only real numbers were related to measurable physical quantities. However, research conducted by the team of Dr. Alexander Streltsov from the Centre 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, found quantum states of entangled photons that cannot be distinguished without resorting to complex numbers. Moreover, the researchers also conducted an experiment confirming the importance of complex numbers for quantum mechanics. Articles describing the theory and measurements have just appeared in the journals Physical Review Letters and Physical Review A.
"In physics, complex numbers were considered to be purely mathematical in nature. It is true that although they play a basic role in quantum mechanics equations, they were treated simply as a tool, something to facilitate calculations for physicists. Now, we have theoretically and experimentally proved that there are quantum states that can only be distinguished when the calculations are performed with the indispensable participation of complex numbers," explains Dr. Streltsov.
Complex numbers are made up of two components, real and imaginary. They have the form a + bi, where the numbers a and b are real. The bi component is responsible for the specific features of complex numbers. The key role here is played by the imaginary number i, i.e. the square root of -1.
There is nothing in the physical world that can be directly related to the number i. If there are 2 or 3 apples on a table, this is natural. When we take one apple away, we can speak of a physical deficiency and describe it with the negative integer -1. We can cut the apple into two or three sections, obtaining the physical equivalents of the rational numbers 1/2 or 1/3. If the table is a perfect square, its diagonal will be the (irrational) square root of 2 multiplied by the length of the side. At the same time, with the best will in the world, it is still impossible to put i apples on the table.
The surprising career of complex numbers in physics is related to the fact that they can be used to describe all sorts of oscillations much more conveniently than with the use of popular trigonometric functions. Calculations are therefore carried out using complex numbers, and then at the end only the real numbers in them are taken into account.
Compared to other physical theories, quantum mechanics is special because it has to describe objects that can behave like particles under some conditions, and like waves in others. The basic equation of this theory, taken as a postulate, is the Schrödinger equation. It describes changes in time of a certain function, called the wave function, which is related to the probability distribution of finding a system in a specific state. However, the imaginary number i openly appears next to the wave function in the Schrödinger equation.
"For decades, there has been a debate as to whether one can create coherent and complete quantum mechanics with real numbers alone. So, we decided to find quantum states that could be distinguished from each other only by using complex numbers. The decisive moment was the experiment where we created these states and physically checked whether they were distinguishable or not," says Dr. Streltsov, whose research was funded by the Foundation for Polish Science.
The experiment verifying the role of complex numbers in quantum mechanics can be presented in the form of a game played by Alice and Bob with the participation of a master conducting the game. Using a device with lasers and crystals, the game master binds two photons into one of two quantum states, absolutely requiring the use of complex numbers to distinguish between them. Then, one photon is sent to Alice and the other to Bob. Each of them measures their photon and then communicates with the other to establish any existing correlations.
"Let's assume Alice and Bob's measurement results can only take on the values of 0 or 1. Alice sees a nonsensical sequence of 0s and 1s, as does Bob. However, if they communicate, they can establish links between the relevant measurements. If the game master sends them a correlated state, when one sees a result of 0, so will the other. If they receive an anti-correlated state, when Alice measures 0, Bob will have 1. By mutual agreement, Alice and Bob could distinguish our states, but only if their quantum nature was fundamentally complex," says Dr. Streltsov.
An approach known as quantum resource theory was used for the theoretical description. The experiment itself with local discrimination between entangled two-photon states was carried out in the laboratory at 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, indelible part of quantum mechanics.
The achievement of the Polish-Chinese-Canadian team of researchers is of fundamental importance, but it is so profound that it may translate into new quantum technologies. In particular, research into the role of complex numbers in quantum mechanics can help to better understand the sources of the efficiency of quantum computers, qualitatively new computing machines capable of solving some problems at speeds unattainable by classical computers.
The Centre for Quantum Optical Technologies at the University of Warsaw (UW) is a unit of the International Research Agendas program implemented by the Foundation for Polish Science from the funds of the Intelligent Development Operational Programme. The seat of the unit is the Centre of New Technologies at the University of Warsaw. The unit conducts research on the use of quantum phenomena such as quantum superposition or entanglement in optical technologies. These phenomena have potential applications in communications, where they can ensure the security of data transmission, in imaging, where they help to improve resolution, and in metrology to increase the accuracy of measurements. The Centre for Quantum Optical Technologies at the University of Warsaw is actively looking for opportunities to cooperate with external entities in order to use the research results in practice.
INFORMATION:
CONTACTS:
Dr. Alexander Streltsov
Centre for Quantum Optical Technologies, University of Warsaw
tel.: +48 22 5543792
email: a.streltsov@cent.uw.edu.pl
SCIENTIFIC PUBLICATIONS:
"Operational Resource Theory of Imaginarity"
K.-D. Wu, T. V. Kondra, S. Rana, C. M. Scandolo, G.-Y. Xiang, Ch.-F. Li, G.-C. Guo, A. Streltsov
Physical Review Letters 126, 090401 (2021)
DOI: 10.1103/PhysRevLett.126.090401
"Resource theory of imaginarity: Quantification and state conversion"
K.-D. Wu, T. V. Kondra, S. Rana, C. M. Scandolo, G.-Y. Xiang, Ch.-F. Li, G.-C. Guo, A. Streltsov
Physical Review A 103, 032401 (2021)
DOI: 10.1103/PhysRevA.103.032401
LINKS:
https://qot.uw.edu.pl/
The website of the Centre for Quantum Optical Technologies, University of Warsaw.
Researchers at Lund University in Sweden have investigated how the X and Y chromosomes evolve and adapt to each other within a population. The results show that breaking up coevolved sets of sex chromosomes could lead to lower survival rates among the offspring - something that could be of importance in species conservation, for example. The study is published in the journal PNAS.
The results provide new clues on how species are formed, and suggest it could be harmful to bring together individuals from different populations that have been separated for a long time. The reason is that the offspring have lower survival rates.
"This is something worth keeping in mind in conservation biology, where you want to see a population ...
By clearing forests, burning grasslands, plowing fields and harvesting crops, humans apply strong selective pressures on the plants that survive on the landscapes we use. Plants that evolved traits for long-distance seed-dispersal, including rapid annual growth, a lack of toxins and large seed generations, were more likely to survive on these dynamic anthropogenic landscapes. In the current article, researchers argue that these traits may have evolved as adaptations for megafaunal mutualisms, later allowing those plants to prosper among increasingly sedentary human populations.
The new study hypothesizes that the presence of specific anthropophilic traits explains why a select few plant families came to dominate the crop and weed ...
The claim that old-growth forests play a significant role in climate mitigation, based upon the argument that even the oldest forests keep sucking CO2 out of the atmosphere, is being refuted by researchers at the University of Copenhagen. The researchers document that this argument is based upon incorrectly analysed data and that the climate mitigation effect of old and unmanaged forests has been greatly overestimated. Nevertheless, they reassert the importance of old-growth forest for biodiversity.
Old and unmanaged forest has become the subject of much debate in ...
One big challenge for the production of synthetic cells is that they must be able to divide to have offspring. In the journal Angewandte Chemie, a team from Heidelberg has now introduced a reproducible division mechanism for synthetic vesicles. It is based on osmosis and can be controlled by an enzymatic reaction or light.
Organisms cannot simply emerge from inanimate material ("abiogenesis"), cells always come from pre-existing cells. The prospect of synthetic cells newly built from the ground up is shifting this paradigm. However, one obstacle on this path is the question of controlled division--a requirement for having "progeny".
A team from the Max Planck Institute for Medical Research in Heidelberg, Heidelberg ...
The team of researchers at Kaunas University of Technology (KTU), Lithuania applied artificial intelligence (AI) methods to evaluate data of human embryo development. The AI-based system photographs the embryos every five minutes, processes the data of their development and notifies any anomalies observed. This increases the likelihood of choosing the most viable and healthy early-stage embryo for IVF procedures. The innovation was developed in collaboration with Esco Medical Technologies, a manufacturer of medical equipment.
Almost one in six couples face infertility; about 48.5 million couples, 186 million individuals worldwide are inflicted. Europe has one of the lowest birth rates in the world, with an average of just 1.55 children per woman.
The most effective form of ...
By offering a microscopic "tightrope" to cells, Virginia Tech and Johns Hopkins University researchers have brought new insights to the way migrating cells interact in the body. The researchers changed their testing environment for observing cell-cell interaction to more closely mirror the body, resulting in new observations of cells interacting like cars on a highway -- pairing up, speeding up, and passing one another.
Understanding the ways migrating cells react to one another is essential to predicting how cells change and evolve and how they react in applications, such as wound healing and drug delivery. In a study published in the Proceedings of the National Academy of Sciences, a team formed by Mechanical Engineering Associate ...
Scientists of Tomsk Polytechnic University jointly with colleagues from different countries have developed a new sensor with two layers of nanopores. In the conducted experiments, this sensor showed its efficiency as a sensor for one of the doping substances from chiral molecules. The research findings are published in Biosensors and Bioelectronics (IF: 10,257; Q1) academic journal.
The material is a thick wafer with pores of 20-30 nm in diameter. The scientists grew a layer of metal-organic frameworks (MOF) from Zn ions and organic molecules on these thick wafers. The MOF has about 3 nm nanopores only. It plays the role of a trap for molecules, which must be detected.
"This sensor can operate with chiral molecules. Such substances consisting of chiral molecules are a lot among medical ...
In the future, photovoltaic cells could be "worn" over clothes, placed on cars or even on beach umbrellas. These are just some of the possible developments from a study published in Nature Communications by researchers at the Physics Department of the Politecnico di Milano, working with colleagues at the University of Erlangen-Nuremberg and Imperial College London.
The research includes among its authors the Institute of Photonics and Nanotechnology (IFN-CNR) researcher Franco V. A. Camargo and Professor Giulio Cerullo. It focused on photovoltaic cells made using flexible organic technology. Today's most popular photovoltaic cells, based on silicone technology, are rigid and ...
The Miscanthus genus of grasses, commonly used to add movement and texture to gardens, could quickly become the first choice for biofuel production. A new study shows these grasses can be grown in lower agricultural grade conditions - such as marginal land - due to their remarkable resilience and photosynthetic capacity at low temperatures.
Miscanthus is a promising biofuel thanks to its high biomass yield and low input requirements, which means it can adapt to a wide range of climate zones and land types. It is seen as a viable commercial option for farmers but yields ...
Energy models are used to explore different options for the development of energy systems in virtual "laboratories". Scientists have been using energy models to provide policy advice for years. As a new study shows, energy models influence policymaking around the energy transition. Similarly, policymakers influence the work of modellers. Greater transparency is needed to ensure that political considerations do not set the agenda for future research or determine its findings, the researchers demand.
Renewable energies bring many changes, including fluctuations in the energy supply and a more geographically distributed generation system. ...
