# A note on the complexity of a phaseless polynomial interpolation

## TL;DR

This paper explores a modified polynomial interpolation problem where evaluations are known only up to a phase factor, demonstrating that polynomial recovery remains feasible in polynomial time under this new setting.

## Contribution

It introduces a novel phase-agnostic interpolation framework and proves that polynomial recovery is computationally efficient in this context.

## Key findings

- Phaseless polynomial interpolation is solvable in polynomial time.
- The new setting extends classical interpolation by incorporating group actions.
- Efficient algorithms are possible for phase-agnostic polynomial recovery.

## Abstract

In this paper we revisit the classical problem of polynomial interpolation, with a slight twist; namely, polynomial evaluations are available up to a group action of the unit circle on the complex plane. It turns out that this new setting allows for a phaseless recovery of a polynomial in a polynomial time.