Mutual Information Across Quantum Reference Frame Perspectives
Abstract
In quantum information theory, standard notions typically presuppose a fixed partition of the world into subsystems, encoded in a tensor product structure of the Hilbert space. Yet, in some scenarios, the subsystem structure is not uniquely fixed. A case in point is the description of subsystems relative to different quantum reference frames (QRFs), where the tensor product structure, although fixed in a specific QRF, changes across different QRFs. Such a relativity of subsystems underlies many interesting features of QRFs, such as the relativity of entanglement, entropy, and coherence. It also raises a broader question: how do we compare the information across different subsystem perspectives, especially when the corresponding subsystem algebras overlap? Here, we propose a notion of quantum mutual information across different QRF perspectives, which captures the correlations between subsystems relative to different frames of reference. To do so, we focus on an algebraic definition of subsystems. Studying in detail the union and overlap between subsystem algebras relative to different QRFs, we find that the usual definition of mutual information in terms of the chain law overcounts the information associated to the overlap. Based on this insight, we propose a modified chain law and show that the resulting notion of mutual information satisfies subadditivity and connects naturally to other measures found in the literature [1]. Our investigations not only provide a way to quantify the relation between different QRF perspectives from an information-theoretic point of view but also sheds light on some important features of quantum information in absence of a fixed tensor product structure.
Related
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- Correlation Harvesting by Unruh--DeWitt Detectors in a Cylindrical Cavity: Entanglement, Mutual Information, and Quantum Discord
- Monogamous quantum corrections to holographic mutual information
- Bosonic Quantum Conditional Mutual Information and Bose-Einstein Condensation
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BibTeX
@misc{valente2026mutual,
title = {{Mutual Information Across Quantum Reference Frame Perspectives}},
author = {Leonardo Valente and Carla Ferradini and Flaminia Giacomini and Viktoria Kabel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31729},
eprint = {2610.31729},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31729},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mutual Information Across Quantum Reference Frame Perspectives
AU - Leonardo Valente
AU - Carla Ferradini
AU - Flaminia Giacomini
AU - Viktoria Kabel
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31729
UR - https://arxiv.org/abs/2610.31729
AB - In quantum information theory, standard notions typically presuppose a fixed partition of the world into subsystems, encoded in a tensor product structure of the Hilbert space. Yet, in some scenarios, the subsystem structure is not uniquely fixed. A case in point is the description of subsystems relative to different quantum reference frames (QRFs), where the tensor product structure, although fixed in a specific QRF, changes across different QRFs. Such a relativity of subsystems underlies many interesting features of QRFs, such as the relativity of entanglement, entropy, and coherence. It also raises a broader question: how do we compare the information across different subsystem perspectives, especially when the corresponding subsystem algebras overlap? Here, we propose a notion of quantum mutual information across different QRF perspectives, which captures the correlations between subsystems relative to different frames of reference. To do so, we focus on an algebraic definition of subsystems. Studying in detail the union and overlap between subsystem algebras relative to different QRFs, we find that the usual definition of mutual information in terms of the chain law overcounts the information associated to the overlap. Based on this insight, we propose a modified chain law and show that the resulting notion of mutual information satisfies subadditivity and connects naturally to other measures found in the literature [1]. Our investigations not only provide a way to quantify the relation between different QRF perspectives from an information-theoretic point of view but also sheds light on some important features of quantum information in absence of a fixed tensor product structure.
ER -