One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance." These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? One important feature of quantum theory is that it has a classical limit, recovering classical theory through the process of decoherence. We show that any theory with a classical limit must contain entangled states, thus establishing entanglement as an inevitable feature of any theory superseding classical theory.
One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance." These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? One important feature of quantum theory is that it has a classical limit, recovering classical theory through the process of decoherence. We show that any theory with a classical limit must contain entangled states, thus establishing entanglement as an inevitable feature of any theory superseding classical theory.
Abstract Einstein introduced quantum entanglement in 1935 and referred to it as “spooky actions at a distance” because it seemed to conflict with his theory of special relativity. Today, some refer to it as “the greatest mystery in physics,” and the 2022 Physics Nobel Prize was even awarded for experimental confirmation of the “spookiness.” While the mystery is experimentally well established, its solution remains elusive because it is commonly believed that quantum entanglement entails one or more of the following: In this book, a rigorous solution to the mystery of quantum entanglement is provided that entails none of those things. The key to this seemingly impossible feat is—to use Einstein’s own language—a “principle” explanation that foregoes the need for any “constructive” explanation of quantum entanglement, such as those listed above. Ironically, the proposed principle explanation is Einstein’s own relativity principle as grounded in quantum information theory. So, contrary to popular belief, quantum mechanics and special relativity are far from inconsistent, as both are a consequence of the exact same relativity principle.
The study of nature at the smallest scales, known as quantum physics, has uncovered occurrences that defy conventional wisdom. Among them, one of the most enigmatic and exciting discoveries is quantum entanglement. When two or more particles become correlated to the point that, regardless of the distance between them, the state of one particle is instantly connected to the state of the other, this is known as entanglement. Once referred to by Einstein as "spooky action at a distance," this phenomenon has developed from a theoretical curiosity to a fundamental component of contemporary quantum technologies. Next-generation communication technologies are among its most revolutionary uses. The power of computational devices using silicon-based integrated circuits has advanced dramatically during the last few decades. Since the gadgets' size will soon approach atomic scales, this remarkable technological advancement based on the principles of classical physics cannot continue eternally. Quantum mechanics would control how these devices operate at these extreme natural regimes. In order to demonstrate drastically new kinds of computing and communication with quantum mechanical states of physical systems, physicists and computer scientists have developed concepts that take advantage of the quantum mechanical behavior of these devices. A basic and fascinating phenomenon in quantum mechanics, quantum entanglement occurs when two or more particles become correlated to the point where the state of one instantly affects the state of the other, regardless of the distance between them. This study explores the theoretical underpinnings of quantum entanglement, including its mathematical formulation, important experimental validations, and implications for new technologies. We will talk about this in this paper. Quantum communication via quantum entanglement.
Introduction The historical development of scientific progress teaches us that every theory that was established and broadly accepted at a certain time was later inevitably replaced by a deeper and more fundamental theory of which the old one remains a special case. One celebrated example is Newtonian (classical) mechanics, which was superseded by quantum mechanics at the beginning of the last century. It is natural to ask whether in a similar manner there could be logically consistent theories that are more generic than quantum theory itself. It could then turn out that quantum mechanics is an effective description of such a theory, only valid within our current restricted domain of experience. At present, quantum theory has been tested against very specific alternative theories that, both mathematically and in their concepts, are distinctly different. Instances of such alternative theories are non-contextual hidden-variable theories [1], local hidden-variable theories [2], crypto-nonlocal hidden-variable theories [3, 4], or some nonlinear variants of the Schrödinger equation [5–8]. Currently, many groups are working on improving experimental conditions to be able to test alternative theories based on various collapse models [9–14]. The common trait of all these proposals is to suppress one or the other counterintuitive feature of quantum mechanics and thus keep some of the basic notions of a classical worldview intact. Specifically, hidden-variable models would allow us to preassign definite values to outcomes of all measurements; collapse models are mechanisms for restraining superpositions between macroscopically distinct states, and nonlinear extensions of the Schrödinger equation may admit more localized solutions for wave-packet dynamics, thereby resembling localized classical particles.
A quantum entangled state is a quantum superposition state. The principle of quantum superposition, and therefore the existence of quantum entanglement, is contingent upon the validity of quantum theory. Thus, the generation of quantum entanglement requires that interactions occur between small-mass particles localized in a confined spatial region, resulting in each particle’s quantum state being a bound state. In other words, the prerequisite for the validity of quantum theory must be satisfied. At the same time, conserved quantities must exist between quantum superposition states, as only quantum states with conserved quantities can undergo superposition, allowing the particle system to generate quantum entangled states. Quantum entangled states can occur between electrons within an atom, between atoms, between molecules, or between atoms and molecules. Within the atomic nucleus, quantum entanglement can exist among protons, neutrons, and the quarks. In superconductivity, superfluidity, and Bose-Einstein condensation, they manifest as macroscopic quantum entanglement, which respectively come from the statistical results of a large amount of microscopic quantum entanglement between electrons, atoms or molecules. For massive macroscopic objects, they exhibit classical properties that cannot be described by quantum theory, and the principle of quantum superposition does not hold. Therefore, no entangled state is generated. It should be particularly emphasized that even for microscopic particle systems, if they exist in a large spatial region, they cannot be described by quantum theory. In such cases, the quantum superposition principle does not hold, and quantum entanglement phenomena do not exist. Therefore, within a large spatial region, multi-electron, multi-photon, and other microscopic systems do not have quantum entangled states; under certain conditions, quantum correlated states can be generated. Consequently, in a large spatial region, the mainstream viewpoints about non-locality—such as the so-called instantaneous collapse of entangled particles during measurement, infinite propagation speed, and the “spooky action at a distance”—are all incorrect. In experiments related to quantum communication and the verification of Bell’s inequality, the quantum states used are quantum correlated states rather than quantum entangled states. Regardless of whether the systems are microscopic or macroscopic, phenomena occurring in a large spatial region must adhere to the principles of causality, realism, and locality. In other words, Einstein’s viewpoint is correct.
Quantum entanglement is popularly believed to give rise to spooky action at a distance of a kind that Einstein decisively rejected. Indeed, important recent experiments on systems assigned entangled states have been claimed to refute Einstein by exhibiting such spooky action. After reviewing two considerations in favor of this view I argue that quantum theory can be used to explain puzzling correlations correctly predicted by assignment of entangled quantum states with no such instantaneous action at a distance. We owe both considerations in favor of the view to arguments of John Bell. I present simplified forms of these arguments as well as a game that provides insight into the situation. The argument I give in response turns on a prescriptive view of quantum states that differs both from Dirac’s (as stated in Chapter 2) and Einstein’s.