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- Gleasons_theorem abstract "Gleason's theorem (named after Andrew M. Gleason) is a mathematical result which is of particular importance for the field of quantum logic. It proves that the Born rule for the probability of obtaining specific results for a given measurement follows naturally from the structure formed by the lattice of events in a real or complex Hilbert space. The theorem states:Theorem. Suppose H is a separable Hilbert space of complex dimension at least 3. Then for any quantum probability measure on the lattice Q of self-adjoint projection operators on H there exists a unique trace class operator W such that P(E) = Tr(W E) for any self-adjoint projection E in Q.The lattice of projections Q can be interpreted as the set of quantum propositions, each proposition having the form \"a ≤ A ≤ b\", where A is the measured value of some observable on H (given by a self-adjoint linear operator). The trace-class operator W can be interpreted as the density matrix of a quantum state. Effectively, the theorem says that any legitimate probability measure on the space of allowable propositions is generated by some quantum state. This implies that the Standard Quantum Logic can be viewed as a manifold of interlocking perspectives that cannot be embedded into a single perspective [Edwards]. Hence, the perspectives cannot be viewed as perspectives on one real world. So, even considering one world as a methodological principle breaks down in the quantum micro-domain.".
- Gleasons_theorem wikiPageExternalLink g047367766j30t07.
- Gleasons_theorem wikiPageExternalLink solers_theorem.html.
- Gleasons_theorem wikiPageExternalLink qt-quantlog.
- Gleasons_theorem wikiPageExternalLink 56050.
- Gleasons_theorem wikiPageID "6796998".
- Gleasons_theorem wikiPageLength "9659".
- Gleasons_theorem wikiPageOutDegree "61".
- Gleasons_theorem wikiPageRevisionID "703645783".
- Gleasons_theorem wikiPageWikiLink Andrew_M._Gleason.
- Gleasons_theorem wikiPageWikiLink Boolean_algebra.
- Gleasons_theorem wikiPageWikiLink Born_rule.
- Gleasons_theorem wikiPageWikiLink Category:Hilbert_space.
- Gleasons_theorem wikiPageWikiLink Category:Probability_theorems.
- Gleasons_theorem wikiPageWikiLink Category:Quantum_measurement.
- Gleasons_theorem wikiPageWikiLink Classical_mechanics.
- Gleasons_theorem wikiPageWikiLink Closure_(mathematics).
- Gleasons_theorem wikiPageWikiLink Complex_number.
- Gleasons_theorem wikiPageWikiLink Connected_space.
- Gleasons_theorem wikiPageWikiLink Countable_set.
- Gleasons_theorem wikiPageWikiLink Density_matrix.
- Gleasons_theorem wikiPageWikiLink Determinism.
- Gleasons_theorem wikiPageWikiLink Dot_product.
- Gleasons_theorem wikiPageWikiLink Field_(mathematics).
- Gleasons_theorem wikiPageWikiLink Hidden_variable_theory.
- Gleasons_theorem wikiPageWikiLink Hilbert_space.
- Gleasons_theorem wikiPageWikiLink Indiana_University_Mathematics_Journal.
- Gleasons_theorem wikiPageWikiLink Information_theory.
- Gleasons_theorem wikiPageWikiLink Inner_product_space.
- Gleasons_theorem wikiPageWikiLink Isomorphism.
- Gleasons_theorem wikiPageWikiLink Lattice_(group).
- Gleasons_theorem wikiPageWikiLink Lattice_(order).
- Gleasons_theorem wikiPageWikiLink Logical_disjunction.
- Gleasons_theorem wikiPageWikiLink Measurement_in_quantum_mechanics.
- Gleasons_theorem wikiPageWikiLink Mutual_exclusivity.
- Gleasons_theorem wikiPageWikiLink Observable.
- Gleasons_theorem wikiPageWikiLink P-adic_quantum_mechanics.
- Gleasons_theorem wikiPageWikiLink Principle_of_bivalence.
- Gleasons_theorem wikiPageWikiLink Propositional_calculus.
- Gleasons_theorem wikiPageWikiLink Quantum_logic.
- Gleasons_theorem wikiPageWikiLink Quantum_state.
- Gleasons_theorem wikiPageWikiLink Quaternion.
- Gleasons_theorem wikiPageWikiLink Real-valued_function.
- Gleasons_theorem wikiPageWikiLink Real_number.
- Gleasons_theorem wikiPageWikiLink Relational_quantum_mechanics.
- Gleasons_theorem wikiPageWikiLink Representation_theorem.
- Gleasons_theorem wikiPageWikiLink Self-adjoint.
- Gleasons_theorem wikiPageWikiLink Self-adjoint_operator.
- Gleasons_theorem wikiPageWikiLink Space_(mathematics).
- Gleasons_theorem wikiPageWikiLink Stochastic.
- Gleasons_theorem wikiPageWikiLink Synthese.
- Gleasons_theorem wikiPageWikiLink Trace_class.
- Gleasons_theorem wikiPageWikiLink Unit_sphere.
- Gleasons_theorem wikiPageWikiLink Vector_space.
- Gleasons_theorem wikiPageWikiLinkText "Gleason's theorem".
- Gleasons_theorem wikiPageWikiLinkText "Gleason’s Theorem".
- Gleasons_theorem date "April 2015".
- Gleasons_theorem reason "Is this L now /all/ of the subspaces of H or only a sublattice?".
- Gleasons_theorem reason "This definition is not really complete.".
- Gleasons_theorem wikiPageUsesTemplate Template:Cite_book.
- Gleasons_theorem wikiPageUsesTemplate Template:Cite_journal.
- Gleasons_theorem wikiPageUsesTemplate Template:What.
- Gleasons_theorem subject Category:Hilbert_space.
- Gleasons_theorem subject Category:Probability_theorems.
- Gleasons_theorem subject Category:Quantum_measurement.
- Gleasons_theorem hypernym Result.
- Gleasons_theorem type Mechanic.
- Gleasons_theorem type Space.
- Gleasons_theorem type Theorem.
- Gleasons_theorem comment "Gleason's theorem (named after Andrew M. Gleason) is a mathematical result which is of particular importance for the field of quantum logic. It proves that the Born rule for the probability of obtaining specific results for a given measurement follows naturally from the structure formed by the lattice of events in a real or complex Hilbert space. The theorem states:Theorem. Suppose H is a separable Hilbert space of complex dimension at least 3.".
- Gleasons_theorem label "Gleason's theorem".
- Gleasons_theorem sameAs Q5567394.
- Gleasons_theorem sameAs m.0gpdh_.
- Gleasons_theorem sameAs Q5567394.
- Gleasons_theorem wasDerivedFrom Gleasons_theorem?oldid=703645783.
- Gleasons_theorem isPrimaryTopicOf Gleasons_theorem.