The Trouble with Weak Values

TL;DR

This paper critically examines the interpretational claims of weak values in quantum theory, arguing that many such claims involve fallacious reasoning and lack a clear, single-system interpretation.

Contribution

It provides a detailed critique of the philosophical and interpretational debates surrounding weak values, clarifying misconceptions and highlighting fallacies.

Findings

Weak values have been used to make exotic claims about quantum systems.

Many interpretational claims about weak values involve fallacious reasoning.

The paper clarifies the distinction between practical applications and interpretational issues.

Abstract

In quantum theory, a weak value is a complex number with a somewhat technical definition: it is a ratio whose numerator is the matrix element of a self-adjoint operator and whose denominator is the inner product of a corresponding pair of state vectors. Weak values first appeared in the research literature in a pair of papers in 1987 and 1988, and were originally defined as the results of a special kind of experimental protocol involving non-disturbing measurements combined with an explicit form of post-selection. In the years since, subsequent papers on weak values have produced a number of important practical spin-offs, including new methods for signal amplification and quantum-state tomography. The present work is not concerned with those practical spin-offs, but with historical and ongoing attempts to assign weak values a transparent, single-system interpretation, as well as efforts that invoke weak values to make a number of exotic claims about the properties and behavior of individual quantum systems. This paper challenges these interpretational claims by arguing that they involve several forms of fallacious reasoning.