We present a method for reconstructing an arbitrary high-dimensional unitary transformation without detecting the qudit that it transforms. We demonstrate the method using orbital angular momentum states of light. Our method relies on quantum interference enabled by path identity of undetected photons. The method is practically useful when suitable detectors are not available for the qudit on which the unitary transformation works.
@article{arxiv.2509.02816,
title = {Characterizing a high-dimensional unitary transformation without measuring the qudit it transforms},
author = {Salini Rajeev and Mayukh Lahiri},
journal= {arXiv preprint arXiv:2509.02816},
year = {2026}
}