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Quantum foundations
Johnie102: Created page and filled it with some preliminary content
Quantum foundations is the study of foundational questions related to [[Quantum mechanics]] and [[Quantum information theory]]. Some problems studied by researchers of quantum foundations are for instance the issue of the correct [[Interpretations of quantum mechanics|interpretation of quantum mechanics]], the [[EPR paradox]] and the related area of [[quantum nonlocality]] and [[contextuality]]. A seminal result in quantum foundations is the existence of [[Bell inequalities]], and later also the [[Kochen–Specker theorem]] that establish a [[no-go theorem]] for certain [[Hidden variable theory|hidden variable interpretations]] of quantum theory.
=== Areas studied in quantum foundations ===
* An [[Interpretations of quantum mechanics|Interpretation of quantum mechanics]] is a description of how the mathematical structure of quantum mechanics corresponds to our physical reality. An interpretation must for instance say whether the quantum [[wave function]] is [[ontic]], i.e. whether it really exists or if it is merely a mathematical artifact and it must also find a way to cope with the existence of [[Quantum entanglement|entanglement]]. Popular interpretations are for instance the [[Copenhagen interpretation]], the [[many-worlds interpretation]] and the [[pilot wave theory]].
* [[Quantum nonlocality]] studies the counterintuitive result that quantum theory allows correlations between spatially separated systems that are stronger then in any classical theory, or even in any [[Local realism|local realist]] description of reality. Nonlocality is an instance of [[quantum contextuality]]. A situation is contextual when the value of an observable depends on the context in which it is measured. There are ways to measure the amount of contextuality of a system<ref>Liquid error: wrong number of arguments (1 for 2)</ref> which leads to the notion of ''strong contextuality'' as is demonstrated in for instance the [[GHZ state]]. Some links between the computational speedup of a [[Quantum Computer]] with respect to a classical computer and the existence of a sufficient amount of contextuality in the computation have also been found.<ref>Liquid error: wrong number of arguments (1 for 2)</ref>
* Supposing that the laws of physics were not governed by quantum mechanics, we might still expect some properties of quantum mechanics to continue to hold. To study which properties, physicists can consider [[foil theories]]<ref></ref>. These are abstract models that might govern the physics of a different universe. For instance, it has been shown that results like the [[No-cloning theorem]] or the existence of incompatible measurements holds in any [[generalised probabilistic theory]] that is not classical<ref>Liquid error: wrong number of arguments (1 for 2)</ref><ref>Liquid error: wrong number of arguments (1 for 2)</ref>. Some well-known foil theories are [[Spekkens toy model]] that is very similar to [[stabilizer quantum theory]] except that it allows a hidden variable model, the strongly nonlocal Popescu-Rohrlich boxes exhibiting even stronger nonlocality than quantum mechanics<ref>Liquid error: wrong number of arguments (1 for 2)</ref> and the [[Euclidean Jordan algebra|Euclidean Jordan algebras]] originally introduced as an algebraic generalisation of the space of observables of quantum theory.
* The [[Mathematical Foundations of Quantum Mechanics]] are not very intuitively sensible. As a result some physicists have taken it upon themselves to find some physical principles from which the laws of quantum mechanics can be derived, similar to how [[Albert Einstein|Einstein]] derived [[General relativity|relativity]] using his [[equivalence principle]]. Although a search for such principles dates back to [[John von Neumann|von Neumann]] and his [[quantum logic]], modern approaches were instigated by Fuchs<ref>Liquid error: wrong number of arguments (1 for 2)</ref> which lead to the first modern [[reconstruction of quantum theory]] by Hardy.<ref>Liquid error: wrong number of arguments (1 for 2)</ref> In his wake other reconstructions using different frameworks and axioms were found.<ref>Liquid error: wrong number of arguments (1 for 2)</ref><ref>Liquid error: wrong number of arguments (1 for 2)</ref>
Other area's of interest are for instance classifying the different types and classes of entanglement, the existence of [[SIC-POVM|SIC-POVMs]] and the study of different types of [[resource theories]].
[[Category:Quantum mechanics]]
[[Category:Quantum physics stubs]]
[[Category:Philosophy of physics]]
=== Areas studied in quantum foundations ===
* An [[Interpretations of quantum mechanics|Interpretation of quantum mechanics]] is a description of how the mathematical structure of quantum mechanics corresponds to our physical reality. An interpretation must for instance say whether the quantum [[wave function]] is [[ontic]], i.e. whether it really exists or if it is merely a mathematical artifact and it must also find a way to cope with the existence of [[Quantum entanglement|entanglement]]. Popular interpretations are for instance the [[Copenhagen interpretation]], the [[many-worlds interpretation]] and the [[pilot wave theory]].
* [[Quantum nonlocality]] studies the counterintuitive result that quantum theory allows correlations between spatially separated systems that are stronger then in any classical theory, or even in any [[Local realism|local realist]] description of reality. Nonlocality is an instance of [[quantum contextuality]]. A situation is contextual when the value of an observable depends on the context in which it is measured. There are ways to measure the amount of contextuality of a system<ref>Liquid error: wrong number of arguments (1 for 2)</ref> which leads to the notion of ''strong contextuality'' as is demonstrated in for instance the [[GHZ state]]. Some links between the computational speedup of a [[Quantum Computer]] with respect to a classical computer and the existence of a sufficient amount of contextuality in the computation have also been found.<ref>Liquid error: wrong number of arguments (1 for 2)</ref>
* Supposing that the laws of physics were not governed by quantum mechanics, we might still expect some properties of quantum mechanics to continue to hold. To study which properties, physicists can consider [[foil theories]]<ref></ref>. These are abstract models that might govern the physics of a different universe. For instance, it has been shown that results like the [[No-cloning theorem]] or the existence of incompatible measurements holds in any [[generalised probabilistic theory]] that is not classical<ref>Liquid error: wrong number of arguments (1 for 2)</ref><ref>Liquid error: wrong number of arguments (1 for 2)</ref>. Some well-known foil theories are [[Spekkens toy model]] that is very similar to [[stabilizer quantum theory]] except that it allows a hidden variable model, the strongly nonlocal Popescu-Rohrlich boxes exhibiting even stronger nonlocality than quantum mechanics<ref>Liquid error: wrong number of arguments (1 for 2)</ref> and the [[Euclidean Jordan algebra|Euclidean Jordan algebras]] originally introduced as an algebraic generalisation of the space of observables of quantum theory.
* The [[Mathematical Foundations of Quantum Mechanics]] are not very intuitively sensible. As a result some physicists have taken it upon themselves to find some physical principles from which the laws of quantum mechanics can be derived, similar to how [[Albert Einstein|Einstein]] derived [[General relativity|relativity]] using his [[equivalence principle]]. Although a search for such principles dates back to [[John von Neumann|von Neumann]] and his [[quantum logic]], modern approaches were instigated by Fuchs<ref>Liquid error: wrong number of arguments (1 for 2)</ref> which lead to the first modern [[reconstruction of quantum theory]] by Hardy.<ref>Liquid error: wrong number of arguments (1 for 2)</ref> In his wake other reconstructions using different frameworks and axioms were found.<ref>Liquid error: wrong number of arguments (1 for 2)</ref><ref>Liquid error: wrong number of arguments (1 for 2)</ref>
Other area's of interest are for instance classifying the different types and classes of entanglement, the existence of [[SIC-POVM|SIC-POVMs]] and the study of different types of [[resource theories]].
[[Category:Quantum mechanics]]
[[Category:Quantum physics stubs]]
[[Category:Philosophy of physics]]
April 14, 2018 at 06:36AM
