Vinzant's Conjecture on Phase Retrieval Injectivity

Vinzant conjectured, in a form later restated by Bandeira, that the $4M-4$ threshold for injective complex phase retrieval is sharp. Part (1) holds: for $A \in \mathbb{C}^{N \times M}$ with $N = 4M-5$ and i.i.d. standard complex Gaussian entries, the phase retrieval map generated by $A$ fails to be injective with positive probability.

Result

Proved(see note)

Status

Partial result

AI contribution

AI-discovered

Method

Argument

Field

Frame theory

Posed by

Cynthia Vinzant; restated by Afonso S. Bandeira

Year posed

—

Years open

—

Solved

2026-06-16

Model

Rethlas

Vendor

—

Collaborators

Zhangsong Li

Verification

Unreviewed

Publication

Preprint

Significance

15 / 100*

Disclosed cost

—

Wikipedia

No dedicated article