On Pauli Pairs

TL;DR

This paper explores the limitations of quantum state distinguishability by constructing new examples of Pauli pairs, showing that certain quantum states cannot be differentiated through position and momentum measurements, contrary to Pauli's conjecture.

Contribution

The paper introduces novel examples of Pauli pairs, including spatially localized states, demonstrating the non-uniqueness of quantum state reconstruction from position and momentum data.

Findings

Constructed new spatially localized Pauli pairs

Provided counterexamples to Pauli's conjecture

Showed quantum states can be indistinguishable by position and momentum measurements

Abstract

The state of a system in classical mechanics can be uniquely reconstructed if we know the positions and the momenta of all its parts. In 1958 Pauli has conjectured that the same holds for quantum mechanical systems. The conjecture turned out to be wrong. In this paper we provide a new set of examples of Pauli pairs, being the pairs of quantum states indistinguishable by measuring the spatial location and momentum. In particular, we construct a new set of spatially localized Pauli pairs.