Phase retrieval by projections in R^n requires 2n-2 projections (This paper has a gap)

TL;DR

This paper proves that at least 2n-2 projections are necessary for phase retrieval in n-dimensional real space, resolving a major open problem in the field.

Contribution

It establishes a sharp lower bound of 2n-2 projections needed for phase retrieval in R^n, filling a key gap in the theoretical understanding.

Findings

Proves the necessity of at least 2n-2 projections for phase retrieval.

Provides a definitive lower bound resolving an open problem.

Advances theoretical understanding of phase retrieval requirements.

Abstract

We will answer the most significant open problem in real phase retrieval by projections by showing it requires at least $2n-2$ projections to do phase retrieval in $\RR^n$.