Phase Retrievability of Super Operators and Measurements
Abstract
We continue the study of Phase Retrieval in the Quantum Information setting in the style of \cite{liu2023phase}, in a manner which is more general in two primary ways: (a) Instead of only pure states we consider also states (and positive semidefinite operators) of bounded rank, as is done in Quantum Tomography; (b) We consider general super operators instead of only quantum channels. We show that in order to have phase retrieval with respect to positive semidefinite operators of bounded rank, it suffices to discriminate between perfectly distinguishable pairs (i.e. those with orthogonal supports). From this we prove that phase retrievability is always Lipschitz stable with respect to the trace norm, and then we use the Fuchs-van de Graaf inequalities to deduce stability with respect to the Bures--Wasserstein distance (thus generalizing the known stability results for phase retrieval in Frame Theory). For Hermitian-preserving super operators taking values in block-diagonal matrices, we characterize phase retrievability in terms of conditions inspired by the classical complement property from Frame Theory.
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BibTeX
@misc{chavezdominguez2026phase,
title = {{Phase Retrievability of Super Operators and Measurements}},
author = {Javier Alejandro Chávez-Domínguez and Jeremiah Ifeanyi Isu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.26474},
eprint = {2607.26474},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.26474},
}
RIS
TY - UNPB
TI - Phase Retrievability of Super Operators and Measurements
AU - Javier Alejandro Chávez-Domínguez
AU - Jeremiah Ifeanyi Isu
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2607.26474
UR - https://arxiv.org/abs/2607.26474
AB - We continue the study of Phase Retrieval in the Quantum Information setting in the style of \cite{liu2023phase}, in a manner which is more general in two primary ways: (a) Instead of only pure states we consider also states (and positive semidefinite operators) of bounded rank, as is done in Quantum Tomography; (b) We consider general super operators instead of only quantum channels. We show that in order to have phase retrieval with respect to positive semidefinite operators of bounded rank, it suffices to discriminate between perfectly distinguishable pairs (i.e. those with orthogonal supports). From this we prove that phase retrievability is always Lipschitz stable with respect to the trace norm, and then we use the Fuchs-van de Graaf inequalities to deduce stability with respect to the Bures--Wasserstein distance (thus generalizing the known stability results for phase retrieval in Frame Theory). For Hermitian-preserving super operators taking values in block-diagonal matrices, we characterize phase retrievability in terms of conditions inspired by the classical complement property from Frame Theory.
ER -