Entanglement
Introduction
Quantum entanglement is a physical phenomenon that occurs when a pair or group of particles interact in ways such that the quantum state of each particle cannot be described independently of the state of the others, even when the particles are separated by a large distance. The topic of entanglement is central to the field of quantum mechanics, and has important implications for areas such as quantum computing, quantum cryptography, and quantum teleportation.
History
The concept of entanglement was first introduced by Albert Einstein, Boris Podolsky, and Nathan Rosen in 1935, in a paper commonly referred to as the EPR paradox. They used the theory of entanglement to argue against the completeness of quantum mechanics, presenting it as a paradox. However, subsequent work by other physicists, most notably John Bell, showed that the EPR paradox did not disprove quantum mechanics, but rather highlighted some of its most non-intuitive aspects.
Theory
Entanglement is a consequence of the superposition principle in quantum mechanics, which states that a physical system—such as a group of particles—can exist in multiple states simultaneously. When a measurement is made on one of the particles, the state of the other particles is instantly affected, no matter the distance between them. This phenomenon, known as "spooky action at a distance" by Einstein, is one of the most intriguing aspects of entanglement.
Mathematical Description
The mathematical description of entanglement involves the use of Hilbert spaces, wave functions, and tensor products. The state of an entangled system is described by a point in a high-dimensional Hilbert space, which is a complex vector space equipped with an inner product. The state of the system is represented by a wave function, which is a mathematical function that provides the probability distribution of the outcomes of measurements made on the system.
Entanglement and Information
One of the most fascinating aspects of entanglement is its implications for information transfer. In theory, entanglement could be used to transmit information instantaneously across vast distances. This has led to the development of the field of quantum information theory, which seeks to understand the fundamental nature of information in the quantum realm.
Applications
Entanglement has numerous potential applications, many of which are still in the experimental stage. These include quantum computing, where entanglement can be used to perform computations at speeds far exceeding those of classical computers; quantum cryptography, which uses entanglement to create unbreakable encryption codes; and quantum teleportation, which could potentially allow for the transmission of quantum states over large distances.