Invariants in Linear Optics
Quantum Physics
2025-09-04 v2
Abstract
Linear optics (LO) prohibits certain transformations. In this paper, we study the conditions for a computation to be possible in LO. We find that there are finitely many polynomials such that each of these polynomials evaluates to the same value on two photonic states if and only if there is a LO circuit transforming one of these states into the other. The proof is non-constructive, so we then focus on methods to find such polynomials.
Keywords
Cite
@article{arxiv.2509.02211,
title = {Invariants in Linear Optics},
author = {Sébastien Draux and Simon Perdrix and Emmanuel Jeandel and Shane Mansfield},
journal= {arXiv preprint arXiv:2509.02211},
year = {2025}
}