Information and Foundations Results
Information and foundations results identify constraints that are easy to overstate. This released card set covers Bell locality, the CHSH witness, noncontextual sharp values, and exact broadcasting of state families.
These cards are lookup entries. They state the theorem, its assumptions, the physical meaning, common misreadings, and links to the pages that own the underlying state, measurement, or channel formalism.
Use Foundations and Interpretations for the guided conceptual route and Foundational Theorems for the rigorous theorem route.
Helpful background. For full derivations, consult Bell’s Theorem for the locality and setting-independence assumptions, Kochen–Specker Theorem for the obstruction to global noncontextual sharp values, and No-Broadcasting Theorem for the exact broadcastability criterion. The cards themselves remain usable as compact lookups.
- CHSH Inequality is the standard two-party, two-setting, two-outcome Bell inequality and the most common quantitative entry point.
- Bell Theorem separates quantum correlations from local hidden-variable models under explicit locality and setting-independence assumptions.
- Kochen–Specker Theorem rules out noncontextual global value assignments preserving the functional structure of projective measurements.
- No-Broadcasting Theorem gives the mixed-state generalization: exactly broadcastable state families are commuting families.
Assumption Discipline
Section titled “Assumption Discipline”No-go theorem language is only useful when the ruled-out task or model is stated precisely. No-broadcasting does not forbid a known singleton or a commuting family. “Bell nonlocality” does not mean controllable faster-than-light signaling. “Kochen–Specker contextuality” does not rule out every hidden-variable theory; it rules out noncontextual value assignments of a specified kind.
For reference use, identify:
- the state set or measurement set being considered;
- whether the process must be exact, deterministic, and universal;
- whether the model assumes locality, noncontextuality, measurement independence, or outcome determinism;
- whether the conclusion concerns probabilities, individual values, channels, or experiments;
- whether a statement is a theorem of the formalism or an experimental test of auxiliary assumptions.
Canonical owners and prerequisites
Section titled “Canonical owners and prerequisites”- Bell Locality and Quantum Correlations owns the Bell-local model, CHSH derivation, and Bell theorem.
- Contextuality and No-Go Results owns contextuality and Kochen–Specker.
- Density Operators, Partial Trace, and Quantum Operations supply the no-broadcasting formalism.
- Projectors, Projection-Valued Measures, and Gleason’s Theorem supply the sharp-event probability structure.
References
Section titled “References”- J. S. Bell, “On the Einstein Podolsky Rosen Paradox,” Physics 1, 195-200, 1964.
- J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Physical Review Letters 23, 880-884, 1969.
- S. Kochen and E. P. Specker, “The Problem of Hidden Variables in Quantum Mechanics,” Indiana University Mathematics Journal 17, 59–87, 1968, doi:10.1512/iumj.1968.17.17004.
- H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa, and B. Schumacher, “Noncommuting mixed states cannot be broadcast,” Physical Review Letters 76, 2818-2821, 1996.
- A. Peres, Quantum Theory: Concepts and Methods, Kluwer, 1995.
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2010.
- J. Watrous, The Theory of Quantum Information, Cambridge University Press, 2018.