Protective Measurement and Quantum Reality

TL;DR

This paper demonstrates how protective measurements allow for the reconstruction of quantum states and observables from single systems, discusses the reality of the wave function, and introduces a universal wave function measurement method using gravity.

Contribution

It extends protective measurement to degenerate and many-particle states and provides a universal wave function measurement approach via gravitational fields.

Findings

Reconstruction of Hilbert space structure from single-system measurements

Generalization of protective measurement to complex quantum systems

Refutation of Einstein's ensemble interpretation argument

Abstract

It is shown that from the expectation values of obervables, which can be measured for a single system using protective measurements, the linear structure, inner product, and observables in the Hilbert space can be reconstructed. A universal method of measuring the wave function of a single particle using its gravitational field is given. Protective measurement is generalized to the measurement of a degenerate state and to many particle systems. The question of whether the wave function is real is examined, and an argument of Einstein in favor of the ensemble interpretation of quantum theory is refuted.