What makes quantum clicks special?

Abstract

This is an elaboration about the "extra" advantage of the performance of quantized physical systems over classical ones; both in terms of single outcomes as well as probabilistic predictions. From a formal point of view, it is based upon entities related to (dual) vectors in (dual) Hilbert spaces, as compared to the Boolean algebra of subsets of a set and the additive measures they support.

60 pages, 6 figures, program codes included

References in corpus (31)

• Experimental quantum teleportation
• Hidden Variables and the Two Theorems of John Bell
• A simple test for hidden variables in spin-1 system
• Experimentally testable state-independent quantum contextuality
• State-independent experimental test of quantum contextuality
• Experimental test of quantum contextuality in neutron interferometry
• Translation of Lueders' "Uber die Zustandsanderung durch den Messprozess"
• Strong Kochen-Specker theorem and incomputability of quantum randomness
• Proposed experiment for testing quantum contextuality with neutrons
• Generalizing Tsirelson's bound on Bell inequalities using a min-max principle
• Coherent states, entanglement, and geometric invariant theory
• On small proofs of Bell-Kochen-Specker theorem for two, three and four qubits
• Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden variable theories
• Proof of the Peres conjecture for contextuality
• Logical equivalence between generalized urn models and finite automata
• Geometry of quantum correlations
• Quantum Scholasticism: On Quantum Contexts, Counterfactuals, and the Absurdities of Quantum Omniscience
• Gadget structures in proofs of the Kochen-Specker theorem
• Quantum Hocus Pocus
• New forms of quantum value indefiniteness suggest that incompatible views on contexts are epistemic
• Testing the bounds on quantum probabilities
• Orthogonal Representation of Graphs
• Faithful orthogonal representations of graphs from partition logics
• Automated generation of Kochen-Specker sets
• Hypergraph Contextuality
• Contextuality in Quantum Mechanics: Testing the Klyachko Inequality
• Roots and (re)sources of value (in)definiteness versus contextuality. A contribution to the Pitowsky Volume in memory of Itamar Pitowsky (1950--2010)
• Classical predictions for intertwined quantum observables are contingent and thus inconclusive
• The structure of Bell inequalities
• Finite precision measurement nullifies Euclid's postulates
• Tracing the bounds on Bell-type inequalities

Cited by in corpus (11)

• Quantum Contextuality
• Extensions of Hardy-type true-implies-false gadgets to classically obtain indistinguishability
• Quantum randomness is chimeric
• Unscrambling the Omelette of Quantum Contextuality (PART 1): Preexistent Properties or Measurement Outcomes?
• Noncontextual coloring of orthogonality hypergraphs
• Generalized Greenberger-Horne-Zeilinger arguments from quantum logical analysis
• Extending Kolmogorov's axioms for a generalized probability theory on collections of contexts
• Violating the KCBS inequality with a toy mechanism
• Quantum violation of the Suppes-Zanotti inequalities and "contextuality"
• Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables
• Vector computation