Reassessment of Leggett inequality

TL;DR

This paper reexamines Leggett inequality, clarifying its assumptions and limitations, and discusses its violation by quantum mechanics, contrasting it with Bell inequality and its implications for non-local hidden variable theories.

Contribution

It provides a detailed analysis of Leggett inequality, highlighting that it applies to a class of local theories and does not require outcome independence, unlike Bell inequality.

Findings

Leggett inequality is violated by quantum mechanics.

The theory applies to a class of local theories.

Outcome independence is not necessary for deriving Leggett inequality.

Abstract

Leggett formulated an inequality which seems to generalize the Bell theorem to non-local hidden variable theories. Leggett inequality is violated by quantum mechanics, as was confirmed by experiment. However, a careful analysis reveals that the theory applies to a class of local theory. Contrary to what happens in the derivation of Bell inequality, it is not necessary to make the hypothesis of outcome independence to derive the Leggett inequality.