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In physics, the Leggett inequalities, [1] named for Anthony James Leggett, who derived them, are a related pair of mathematical expressions concerning the correlations of properties of entangled particles. (As published by Leggett, the inequalities were exemplified in terms of relative angles of elliptical and linear polarizations.)
They are fulfilled by a large class of physical theories based on particular non-local and realistic assumptions, that may be considered to be plausible or intuitive according to common physical reasoning.
The Leggett inequalities are violated by quantum mechanical theory. The results of experimental tests in 2007 and 2010 have shown agreement with quantum mechanics rather than the Leggett inequalities. [2] [3] Given that experimental tests of Bell's inequalities have ruled out local realism in quantum mechanics, the violation of Leggett's inequalities is considered to have falsified realism in quantum mechanics. [4] In quantum mechanics "realism" means "notion that physical systems possess complete sets of definite values for various parameters prior to, and independent of, measurement". [5]
Quantum entanglement is the phenomenon of a group of particles being generated, interacting, or sharing spatial proximity in such a way that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. "Local" here refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields cannot propagate faster than the speed of light. "Hidden variables" are putative properties of quantum particles that are not included in quantum theory but nevertheless affect the outcome of experiments. In the words of physicist John Stewart Bell, for whom this family of results is named, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."
John Stewart Bell FRS was a physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories.
Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. Prior to quantum physics, it was thought that
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of instantaneous, or "non-local" action at a distance. Locality evolved out of the field theories of classical physics. The idea is that for a cause at one point to have an effect at another point, something in the space between those points must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence.
A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism. Named for John Stewart Bell, the experiments test whether or not the real world satisfies local realism, which requires the presence of some additional local variables to explain the behavior of particles like photons and electrons. The test empirically evaluates the implications of Bell's theorem. As of 2015, all Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems behave.
Anton Zeilinger is an Austrian quantum physicist and Nobel laureate in physics of 2022. Zeilinger is professor of physics emeritus at the University of Vienna and senior scientist at the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences. Most of his research concerns the fundamental aspects and applications of quantum entanglement.
Alain Aspect is a French physicist noted for his experimental work on quantum entanglement.
In quantum mechanics, superdeterminism is a loophole in Bell's theorem. By postulating that all systems being measured are correlated with the choices of which measurements to make on them, the assumptions of the theorem are no longer fulfilled. A hidden variables theory which is superdeterministic can thus fulfill Bell's notion of local causality and still violate the inequalities derived from Bell's theorem. This makes it possible to construct a local hidden-variable theory that reproduces the predictions of quantum mechanics, for which a few toy models have been proposed. In addition to being deterministic, superdeterministic models also postulate correlations between the state that is measured and the measurement setting.
The Institute for Quantum Optics and Quantum Information (IQOQI) (German: Institut für Quantenoptik und Quanteninformation) is a member institute of the Austrian Academy of Sciences and was founded in November 2003, to create an Austrian research center for the newly developing fields of theoretical and experimental quantum optics and quantum information.
The Leggett–Garg inequality, named for Anthony James Leggett and Anupam Garg, is a mathematical inequality fulfilled by all macrorealistic physical theories. Here, macrorealism is a classical worldview defined by the conjunction of two postulates:
John Francis Clauser is an American theoretical and experimental physicist known for contributions to the foundations of quantum mechanics, in particular the Clauser–Horne–Shimony–Holt inequality. Clauser was awarded the 2022 Nobel Prize in Physics, jointly with Alain Aspect and Anton Zeilinger "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science".
The toric code is a topological quantum error correcting code, and an example of a stabilizer code, defined on a two-dimensional spin lattice. It is the simplest and most well studied of the quantum double models. It is also the simplest example of topological order—Z2 topological order (first studied in the context of Z2 spin liquid in 1991). The toric code can also be considered to be a Z2 lattice gauge theory in a particular limit. It was introduced by Alexei Kitaev.
In physics and the philosophy of physics, quantum Bayesianism is a collection of related approaches to the interpretation of quantum mechanics, the most prominent of which is QBism. QBism is an interpretation that takes an agent's actions and experiences as the central concerns of the theory. QBism deals with common questions in the interpretation of quantum theory about the nature of wavefunction superposition, quantum measurement, and entanglement. According to QBism, many, but not all, aspects of the quantum formalism are subjective in nature. For example, in this interpretation, a quantum state is not an element of reality—instead, it represents the degrees of belief an agent has about the possible outcomes of measurements. For this reason, some philosophers of science have deemed QBism a form of anti-realism. The originators of the interpretation disagree with this characterization, proposing instead that the theory more properly aligns with a kind of realism they call "participatory realism", wherein reality consists of more than can be captured by any putative third-person account of it.
Anupam Kumar Garg is a professor in the department of Physics & Astronomy at Northwestern University, Illinois. Anupam Kumar Garg was born on August 17, 1956 in Amritsar, India. He received his Ph.D. in 1983 from Cornell University. In 2012, he became a Fellow of the American Physical Society (APS) thanks to his work on molecular magnetism and macroscopic quantum phenomena.
Quantum contextuality is a feature of the phenomenology of quantum mechanics whereby measurements of quantum observables cannot simply be thought of as revealing pre-existing values. Any attempt to do so in a realistic hidden-variable theory leads to values that are dependent upon the choice of the other (compatible) observables which are simultaneously measured. More formally, the measurement result of a quantum observable is dependent upon which other commuting observables are within the same measurement set.
Aspect's experiment was the first quantum mechanics experiment to demonstrate the violation of Bell's inequalities with photons using distant detectors. Its 1982 result allowed for further validation of the quantum entanglement and locality principles. It also offered an experimental answer to Albert Einstein, Boris Podolsky, and Nathan Rosen's paradox which had been proposed about fifty years earlier.
Applying classical methods of machine learning to the study of quantum systems is the focus of an emergent area of physics research. A basic example of this is quantum state tomography, where a quantum state is learned from measurement. Other examples include learning Hamiltonians, learning quantum phase transitions, and automatically generating new quantum experiments. Classical machine learning is effective at processing large amounts of experimental or calculated data in order to characterize an unknown quantum system, making its application useful in contexts including quantum information theory, quantum technologies development, and computational materials design. In this context, it can be used for example as a tool to interpolate pre-calculated interatomic potentials or directly solving the Schrödinger equation with a variational method.
Michael Allan Horne was an American quantum physicist, known for his work on the foundations of quantum mechanics.
Robert W. Spekkens is a Canadian theoretical quantum physicist working in the fields of quantum foundations and quantum information.
