Common Denominator for Value and Expectation No-Go Theorems

TL;DR

This paper clarifies the relationship between two types of no-go theorems in quantum hidden-variable theories, focusing on projection measurements to compare their implications for value and expectation predictions.

Contribution

It refines existing no-go theorems by focusing solely on projection measurements, clarifying their differences and similarities in predicting measurement outcomes.

Findings

Expectation no-go theorems do not subsume value no-go theorems.

Both approaches are equally valid and focus on projection measurements.

Clarifies the scope and limitations of hidden-variable theories in quantum mechanics.

Abstract

Hidden-variable (HV) theories allege that a quantum state describes an ensemble of systems distinguished by the values of hidden variables. No-go theorems assert that HV theories cannot match the predictions of quantum theory. The present work started with repairing flaws in the literature on no-go theorems asserting that HV theories cannot predict the expectation values of measurements. That literature gives one an impression that expectation no-go theorems subsume the time-honored no-go theorems asserting that HV theories cannot predict the possible values of measurements. But the two approaches speak about different kinds of measurement. This hinders comparing them to each other. Only projection measurements are common to both. Here, we sharpen the results of both approaches so that only projection measurements are used. This allows us to clarify the similarities and differences between the two approaches. Neither one dominates the other.