Classical Probability and Quantum Outcomes

• Main Author: James D. Malley
• Format: Article
• Language: English
• Published: MDPI AG 2014-05-01
• Series: Axioms
• Subjects: Kochen-Specker; quantum hidden variables; noncontextuality; joint distributions; quantum conditional probability
• Online Access: http://www.mdpi.com/2075-1680/3/2/244

There is a contact problem between classical probability and quantum outcomes. Thus, a standard result from classical probability on the existence of joint distributions ultimately implies that all quantum observables must commute. An essential task here is a closer identification of this conflict based on deriving commutativity from the weakest possible assumptions, and showing that stronger assumptions in some of the existing no-go proofs are unnecessary. An example of an unnecessary assumption in such proofs is an entangled system involving nonlocal observables. Another example involves the Kochen-Specker hidden variable model, features of which are also not needed to derive commutativity. A diagram is provided by which user-selected projectors can be easily assembled into many new, graphical no-go proofs.