On Hidden Variables: Value and Expectation No-Go Theorems

TL;DR

This paper analyzes two types of no-go theorems in quantum mechanics, clarifying their differences and strengthening the existing results about hidden-variable theories' limitations in reproducing quantum predictions.

Contribution

It refines and clarifies the distinctions between value and expectation no-go theorems, and improves the definitions and proofs related to hidden-variable no-go results.

Findings

Sharpened the known results of value and expectation no-go theorems

Clarified the differences and similarities between the two types of theorems

Repaired flaws in existing definitions and proofs

Abstract

No-go theorems assert that hidden-variable theories, subject to appropriate hypotheses, cannot reproduce the predictions of quantum theory. We examine two species of such theorems, value no-go theorems and expectation no-go theorems. The former assert that hidden-variables cannot match the predictions of quantum theory about the possible values resulting from measurements; the latter assert that hidden-variables cannot match the predictions of quantum theory about the expectation values of measurements. We sharpen the known results of both species, which allows us to clarify the similarities and differences between the two species. We also repair some flaws in existing definitions and proofs.