Leggett-Garg inequalities cannot be violated in quantum measurements

TL;DR

This paper proves that Leggett-Garg inequalities, which distinguish classical from quantum behavior, cannot be violated by any projective or weak measurements, challenging previous claims of quantum violations.

Contribution

It demonstrates that Leggett-Garg inequalities cannot be violated by projective or weak measurements, clarifying misconceptions about quantum violations.

Findings

Leggett-Garg inequalities cannot be violated by projective measurements.

Weak projective measurements also do not violate the inequalities.

Previous perceived violations are due to incorrect assumptions about non-invasive measurability.

Abstract

Leggett and Garg derived inequalities that probe the boundaries of classical and quantum physics by putting limits on the properties that classical objects can have. Historically, it has been suggested that Leggett-Garg inequalities are easily violated by quantum systems undergoing sequences of strong measurements, casting doubt on whether quantum mechanics correctly describes macroscopic objects. Here I show that Leggett-Garg inequalities cannot be violated by any projective measurement. The perceived violation of the inequalities found previously can be traced back to an inappropriate assumption of non-invasive measurability. Surprisingly, weak projective measurements cannot violate the Leggett-Garg inequalities either because even though the quantum system itself is not fully projected via weak measurements, the measurement devices are.