The modern theory of quantum mechanics describes the dynamics of a variety of systems as well as possible measurement outcomes. While quantum theory is fundamental and therefore applies to all systems, including macroscopic ones, its prominent effects are not directly visible and have to be revealed by dedicated sensitive measurements. It is often necessary to keep track of possible influences from unintended interactions with the system's surroundings. In contrast to classical physics, which would relate such interactions to small and often negligible exchanges of energy, quantum physics is highly susceptible to such influences because they can change the information potentially gained from a measurement, or they may adversely affect a controlled process such as a quantum computation.
The modern theory of quantum mechanics describes the dynamics of a variety of systems as well as possible measurement outcomes. While quantum theory is fundamental and therefore applies to all systems, including macroscopic ones, its prominent effects are not directly visible and have to be revealed by dedicated sensitive measurements. It is often necessary to keep track of possible influences from unintended interactions with the system's surroundings. In contrast to classical physics, which would relate such interactions to small and often negligible exchanges of energy, quantum physics is highly susceptible to such influences because they can change the information potentially gained from a measurement, or they may adversely affect a controlled process such as a quantum computation.
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. – Max Planck, 1936 The only way quantum theory allows us to interact with quantum systems is via quantum processes. Thus, the only way we can extract information about the state of a quantum system is to apply some non-deterministic process and observe which of the branches happened. For that reason, many people refer to the act of applying certain quantum processes as measurement and sometimes even as observation . A consequence of this unfortunate terminology is that one of the most touted ‘strange’ features of quantum theory is often misleadingly described as follows: ‘The mere act of observing a quantum state changes it.’ ‘Misleading’, since the concept of measurement described in the previous paragraph is far from the passive concept of observation familiar from our macroscopic world, but is rather a non-trivial process that will almost always drastically affect the quantum state. So, the mysterious aspect of quantum theory is not that ‘observation’ alters the quantum state but, rather, that it is impossible, even in principle, to ‘observe’ a quantum system in the classical sense. Given this fundamental restriction on how we can extract information from a quantum system, what can we learn about that system by means of a quantum process? The answer is, in fact, very little! First, performing a particular measurement could, for the vast majority of quantum states, yield any outcome i with a non-zero probability. In that case, obtaining an outcome i doesn't tell us much about what the state of the system was. Second, we say ‘was’, because the measurement will moreover irreversibly change the state according to the outcome. So rather than revealing the state of a system, a quantum measurement typically erases that state from history! Nonetheless, these quantum measurements are crucial to quantum theory since they constitute the only interface between us, in our classical world, and the quantum world. The great insight of the quantum computing community is that the non-deterministic changes induced by these quantum measurements are not a nuisance, but rather an extremely useful resource.
Abstract Measurement lies at the core of the quantum formalism. This may seem a statement of the intuitively obvious for any theoretical structure with a pretension to predict the outcomes of observations made or experiments performed on objects in the real world. But classical mechanics is a theorys of the physical properties of objects and their behaviour when exposed to different kinds of forces, and there is no particularly significant role for measurement other than a passive role involving the recording of those properties or behaviour. In contrast, measurement in quantum theory takes on a far deeper, almost ominous, significance
Changes in the field of quantum theory taking place in modern science have also affected linguistics. Quantum mechanics is one of the major achievements of past difficulties. The object of study of quantum theory is a minimal, weekly particle - a quantum. The functional liquidity of quanta and linguistic units has been revealed, which makes it possible to transfer research from quantum mechanics to the field of cognitive linguistics. The quantum-cognitive approach expands the view of the concept of nature, highlights its quantum properties and allows us to consider its dynamics as a quantum wave process. In the article, the subject of research is the concept, its dynamics as a change in the states of the concept and its interaction in various combinations. The work pays attention to such phenomena as quantum entanglement, quantum nonlocality, measurement, and contextuality. Modeling in the quantum-cognitive aspect involves considering changes in the state of a concept under the influence of context. The state of the concept through the prism of quantum mechanics is considered as a wave function that changes under the influence of context. To apply general methodological approaches to describing both phenomena, we will focus on such phenomena as “quantum uncertainty” and “quantum entanglement.” The article explores the concept through the prism of quantum theory. The material for the study was scientific publications and articles selected by a continuous sampling method on the topics “Quantum Physics”, “Quantum Mechanics”, “Quantum Physics”, “Cognitive Linguistics”. The object of study of the article is the concept as a quantum immaterial cognitive formation that exists in the human mind. The study of the concept is based on a synthesis of the principles of two scientific directions: quantum mechanics and cognitive linguistics.
The introductory basics of quantum mechanics were said to arise from the changes from classical mechanics in the first chapter. In some sense, these changes are brought to an observable level by the smallness of some parameter, such as the size scale. In another sense, however, quantum mechanics introduces some fundamental changes, that are not at all present in classical mechanics. Perhaps the most important effect is the appearance of operators in place of dynamical variables and the non-commuting nature of these operators. While these properties are present in normal mathematics, they are not usually associated with discussions of classical mechanics.
Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the transitional potential is to provide a jump from a deterministic state to a random state with prescribed probability density. This jump is triggered by blowup instability due to violation of Lipschitz condition generated by the quantum potential. As a result, the dynamics attains quantum properties on a classical scale. The model can be implemented physically as an analog VLSI-based (very-large-scale integration-based) computer, or numerically on a digital computer. This work opens a way of developing fundamentally new algorithms for quantum simulations of exponentially complex problems that expand NASA capabilities in conducting space activities. It has been illustrated that the complexity of simulations of particle interaction can be reduced from an exponential one to a polynomial one.
At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.