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Bibliography

A curated collection of key references on Kochen–Specker sets, contextuality, and their connections to quantum computation.

Original Kochen–Specker Theorem

  • S. Kochen and E. P. Specker, "The problem of hidden variables in quantum mechanics," Journal of Mathematics and Mechanics 17, 59–87 (1967)

    • The foundational paper proving that no noncontextual hidden-variable theory can reproduce quantum predictions in dimensions ≥ 3.

  • J. S. Bell, "On the problem of hidden variables in quantum mechanics," Reviews of Modern Physics 38, 447–452 (1966)

    • Bell's discussion of hidden variables, complementing the Kochen–Specker approach.

Kernaghan's 20-Vector KS Set (4D)

  • M. Kernaghan, "Bell–Kochen–Specker theorem for 20 vectors," Journal of Physics A: Mathematical and General 27, L829–L830 (1994)
    • The original construction of the 20-vector KS set in 4-dimensional Hilbert space.

Kernaghan–Peres 40-Vector KS Set (8D)

  • M. Kernaghan and A. Peres, "Kochen–Specker theorem for eight-dimensional space," Physics Letters A 198, 1–5 (1995)
    • The 40-vector construction in 8D, connecting KS proofs to three-qubit systems.

Cabello's 18-Vector Minimal KS Set (4D)

  • A. Cabello, J. M. Estebaranz, and G. García-Alcaine, "Bell–Kochen–Specker theorem: A proof with 18 vectors," Physics Letters A 212, 183–187 (1996)
    • The minimal known KS set in 4 dimensions.

Peres and the Peres–Mermin Square

  • A. Peres, "Two simple proofs of the Kochen–Specker theorem," Journal of Physics A: Mathematical and General 24, L175–L178 (1991)

    • Peres' 33-ray construction in 3D.

  • A. Peres, Quantum Theory: Concepts and Methods, Kluwer Academic Publishers (1993)

    • A comprehensive textbook covering quantum foundations, contextuality, and quantum information.

  • N. D. Mermin, "Hidden variables and the two theorems of John Bell," Reviews of Modern Physics 65, 803–815 (1993)

    • Mermin's pedagogical review, including the magic square argument.

  • N. D. Mermin, "Simple unified form for the major no-hidden-variables theorems," Physical Review Letters 65, 3373–3376 (1990)

    • The Mermin star construction for three qubits.

Generalized Contextuality (Spekkens)

  • R. W. Spekkens, "Contextuality for preparations, transformations, and unsharp measurements," Physical Review A 71, 052108 (2005)

    • The foundational paper on generalized noncontextuality.

  • R. W. Spekkens, "Negativity and contextuality are equivalent notions of nonclassicality," Physical Review Letters 101, 020401 (2008)

    • Establishes the equivalence between contextuality and Wigner function negativity.

  • R. W. Spekkens, "Evidence for the epistemic view of quantum states: A toy theory," Physical Review A 75, 032110 (2007)

    • The epistemic toy model.

  • M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, "An experimental test of noncontextuality without unphysical idealizations," Nature Communications 7, 11780 (2016)

    • Experimental demonstration of generalized contextuality.

  • R. Kunjwal and R. W. Spekkens, "From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism," Physical Review Letters 115, 110403 (2015)

    • Connecting KS-type proofs to operational inequalities.

Contextuality and Quantum Computation

  • M. Howard, J. Wallman, V. Veitch, and J. Emerson, "Contextuality supplies the 'magic' for quantum computation," Nature 510, 351–355 (2014)

    • The seminal paper connecting contextuality (Wigner negativity) to quantum computational advantage.

  • R. Raussendorf, "Contextuality in measurement-based quantum computation," Physical Review A 88, 022322 (2013)

    • Contextuality as a resource for MBQC.

  • J. Anders and D. E. Browne, "Computational power of correlations," Physical Review Letters 102, 050502 (2009)

    • Correlations and computational power in MBQC.

  • V. Veitch, S. A. H. Mousavian, D. Gottesman, and J. Emerson, "The resource theory of stabilizer quantum computation," New Journal of Physics 16, 013009 (2014)

    • Resource-theoretic treatment of magic states.

  • S. Bravyi and A. Kitaev, "Universal quantum computation with ideal Clifford gates and noisy ancillas," Physical Review A 71, 022316 (2005)

    • Magic state distillation and fault-tolerant quantum computation.

  • D. Gottesman, "The Heisenberg representation of quantum computers," arXiv:quant-ph/9807006 (1998)

    • Stabilizer formalism and the Gottesman–Knill theorem.

Graph-Theoretic Approaches

  • A. Cabello, S. Severini, and A. Winter, "Graph-theoretic approach to quantum correlations," Physical Review Letters 112, 040401 (2014)

    • Using graph theory to study contextuality and nonlocality.

  • A. Cabello, "Experimentally testable state-independent quantum contextuality," Physical Review Letters 101, 210401 (2008)

    • Contextuality inequalities for experimental tests.

  • D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Going beyond Bell's theorem," in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M. Kafatos, ed., Kluwer Academic (1989), pp. 69–72

    • The original GHZ paper.

  • D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, "Bell's theorem without inequalities," American Journal of Physics 58, 1131–1143 (1990)

    • Extended discussion of GHZ correlations.

Reviews and Pedagogical Resources

  • A. Cabello, "Kochen–Specker theorem and experimental tests," in Quantum [Un]Speakables II: Half a Century of Bell's Theorem, R. Bertlmann and A. Zeilinger, eds., Springer (2017)

    • A comprehensive review of KS constructions and experiments.

  • M. Budroni, A. Cabello, O. Gühne, M. Kleinmann, and J.-Å. Larsson, "Kochen-Specker contextuality," Reviews of Modern Physics 94, 045007 (2022)

    • A modern review of contextuality research.

  • S. Abramsky and A. Brandenburger, "The sheaf-theoretic structure of non-locality and contextuality," New Journal of Physics 13, 113036 (2011)

    • Mathematical framework for contextuality using sheaf theory.

Additional KS Constructions

  • S. Yu and C. H. Oh, "State-independent proof of Kochen–Specker theorem with 13 rays," Physical Review Letters 108, 030402 (2012)

    • A 13-ray state-dependent construction in 3D.

  • P. K. Aravind, "A simple demonstration of Bell's theorem involving two observers and no probabilities or inequalities," arXiv:quant-ph/0206070 (2002)

    • Pedagogical exposition of KS-type arguments.

  • C. Held, "The Kochen-Specker theorem," Stanford Encyclopedia of Philosophy (2018)

    • Philosophical context and implications.

Experimental Tests

  • G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, "State-independent experimental test of quantum contextuality," Nature 460, 494–497 (2009)

    • Ion trap test of contextuality.

  • E. Amselem, M. Rådmark, M. Bourennane, and A. Cabello, "State-independent quantum contextuality with single photons," Physical Review Letters 103, 160405 (2009)

    • Photonic contextuality experiment.

This bibliography will be expanded as the atlas grows. Suggestions for additional references are welcome.