Quantum Partial Information Decompositions, an Operational Order on Ensembles, and Direct Quantifications of Objective Information
Abstract
The partial information decomposition (PID) framework is an extension of classical information theory that enables a systematic analysis of the structure of information in multipartite systems. We advance a simple extension of this framework enabling the construction of multipartite quantum PIDs (QPIDs); generalizing recent, exclusively bipartite, extensions. We construct two QPIDs of the Holevo quantity. First a naive QPID based on the classical minimum mutual information. Second a sophisticated QPID enabled by our development of an operational partial order on quantum ensembles in terms of ensemble (inter-)convertability. Finally, as a concrete example of how QPIDs can be applied, we investigate objectivity scenarios; using our Holevo QPIDs to directly quantify objective information in extended graph states. These findings ultimately establish a foundation upon which generic multipartite QPIDs can be systematically constructed, introduce an operational partial order on ensembles, advance QPIDs as interesting objects of study in their own right, and demonstrate their immediate applicability to problems in quantum information.
Related
- Colloquium: Quantum information processing with ensembles of identical particles
- An Information-Theoretic Principle for Optimal Quantum Encoding: Tight Frames and Equiangular Ensembles
- Partial projected ensembles reveal slow tilt-constrained information spreading
- Free Mutual Information and Higher-Point Out-of-Time-Ordered Correlators
- The Universe as a Consistency-Constrained Information History: An Interpretive Framework (Akashic Ledger Architecture Cosmology)
BibTeX
@misc{nicokatz2026quantum,
title = {{Quantum Partial Information Decompositions, an Operational Order on Ensembles, and Direct Quantifications of Objective Information}},
author = {Alexander Nico-Katz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20694},
eprint = {2610.20694},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20694},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Partial Information Decompositions, an Operational Order on Ensembles, and Direct Quantifications of Objective Information
AU - Alexander Nico-Katz
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20694
UR - https://arxiv.org/abs/2610.20694
AB - The partial information decomposition (PID) framework is an extension of classical information theory that enables a systematic analysis of the structure of information in multipartite systems. We advance a simple extension of this framework enabling the construction of multipartite quantum PIDs (QPIDs); generalizing recent, exclusively bipartite, extensions. We construct two QPIDs of the Holevo quantity. First a naive QPID based on the classical minimum mutual information. Second a sophisticated QPID enabled by our development of an operational partial order on quantum ensembles in terms of ensemble (inter-)convertability. Finally, as a concrete example of how QPIDs can be applied, we investigate objectivity scenarios; using our Holevo QPIDs to directly quantify objective information in extended graph states. These findings ultimately establish a foundation upon which generic multipartite QPIDs can be systematically constructed, introduce an operational partial order on ensembles, advance QPIDs as interesting objects of study in their own right, and demonstrate their immediate applicability to problems in quantum information.
ER -