Why protective measurement does not establish the reality of the quantum state

TL;DR

This paper critically examines protective measurement in quantum mechanics, arguing that it does not prove the quantum state is an objective reality, by providing counter-arguments and explicit models.

Contribution

The paper presents three novel counter-arguments and constructs explicit models to challenge claims that protective measurement establishes the reality of the quantum state.

Findings

Protective measurement resources can reconstruct quantum states via process tomography.

Explicit $ta$-epistemic models show protective measurement does not imply reality.

Most information in protective measurement comes from the protection operation, not the quantum state.

Abstract

"Protective measurement" refers to two related schemes for finding the expectation value of an observable without disturbing the state of a quantum system, given a single copy of the system that is subject to a "protecting" operation. There have been several claims that these schemes support interpreting the quantum state as an objective property of a single quantum system. Here we provide three counter-arguments, each of which we present in two versions tailored to the two different schemes. Our first argument shows that the same resources used in protective measurement can be used to reconstruct the quantum state in a different way via process tomography. Our second argument is based on exact analyses of special cases of protective measurement, and our final argument is to construct explicit "$\psi$-epistemic" toy models for protective measurement, which strongly suggest that protective measurement does not imply the reality of the quantum state. The common theme of the three arguments is that almost all of the information comes from the "protection" operation rather than the quantum state of the system, and hence the schemes have no implications for the reality of the quantum state.