Identifiability in Quantum State, Process, and Network Tomography
Abstract
Quantum State Tomography (QST), Quantum Process Tomography (QPT), and Quantum Network Tomography (QNT) are related parameter-estimation problems that aim to reconstruct different physical quantities. QST estimates an unknown quantum state, represented by its density matrix, from the measurement outcomes. QPT characterises an unknown quantum channel using known input states and measurements of the corresponding outputs. QNT, in contrast, aims to infer parameters associated with individual links from end-to-end probe measurements collected at accessible monitor nodes. A key distinction among the three tomography problems lies in the conditions required to achieve identifiability, the ability to determine unknown parameters uniquely from the available measurement statistics. In QST and QPT, the experimenter can choose an Informationally Complete (IC) measurement set. QNT limits the reachable measurements to what topology and monitor placement allow, so the admissible probe paths fix the information available about the link parameters. This work studies all three tomography problems through a common Fisher Information Matrix (FIM). We factorise QNT FIM and show that its rank equals the rank of the path-link incidence matrix at every interior parameter value, so local and global identifiability coincide. We then show that QST and QPT attain full rank under IC settings, QNT loses rank when the probe paths leave link parameters indistinguishable, and increasing the number of copies scales the FIM eigenvalues while leaving its rank fixed.
Related
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BibTeX
@misc{raghunadhan2026identifiability,
title = {{Identifiability in Quantum State, Process, and Network Tomography}},
author = {Athira Kalavampara Raghunadhan and Matheus Guedes De Andrade and Don Towsley and Indrakshi Dey and Daniel Kilper and Nicola Marchetti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13584},
eprint = {2609.13584},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13584},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Identifiability in Quantum State, Process, and Network Tomography
AU - Athira Kalavampara Raghunadhan
AU - Matheus Guedes De Andrade
AU - Don Towsley
AU - Indrakshi Dey
AU - Daniel Kilper
AU - Nicola Marchetti
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13584
UR - https://arxiv.org/abs/2609.13584
AB - Quantum State Tomography (QST), Quantum Process Tomography (QPT), and Quantum Network Tomography (QNT) are related parameter-estimation problems that aim to reconstruct different physical quantities. QST estimates an unknown quantum state, represented by its density matrix, from the measurement outcomes. QPT characterises an unknown quantum channel using known input states and measurements of the corresponding outputs. QNT, in contrast, aims to infer parameters associated with individual links from end-to-end probe measurements collected at accessible monitor nodes. A key distinction among the three tomography problems lies in the conditions required to achieve identifiability, the ability to determine unknown parameters uniquely from the available measurement statistics. In QST and QPT, the experimenter can choose an Informationally Complete (IC) measurement set. QNT limits the reachable measurements to what topology and monitor placement allow, so the admissible probe paths fix the information available about the link parameters. This work studies all three tomography problems through a common Fisher Information Matrix (FIM). We factorise QNT FIM and show that its rank equals the rank of the path-link incidence matrix at every interior parameter value, so local and global identifiability coincide. We then show that QST and QPT attain full rank under IC settings, QNT loses rank when the probe paths leave link parameters indistinguishable, and increasing the number of copies scales the FIM eigenvalues while leaving its rank fixed.
ER -