Entropy Concentration and Universal Typicality for Almost i.i.d. Quantum Sources
Abstract
We establish two concentration principles for almost i.i.d. quantum sources under the weakly almost i.i.d. condition, the broadest condition in the established hierarchy of almost i.i.d. sources. Our results therefore apply also to Wasserstein- and Mazzola-Sutter-Renner almost i.i.d. sources. Weakly almost i.i.d. sources are sequences of multipartite states whose fixed-size marginals converge, on average, to tensor powers of a reference state, while allowing arbitrary global correlations and entanglement. We prove a noncommutative weak law of large numbers for empirical observables, and a universal entropy-concentration principle showing asymptotic concentration on subspaces of exponential dimension governed by the von Neumann entropy of the reference state. These concentration principles provide a unified and conceptually transparent approach to several information-theoretic applications beyond the i.i.d. setting, including direct proofs of universal compression within classes of weakly almost i.i.d. sources sharing a common reference state and asymmetric quantum hypothesis-testing bounds. They also yield concentration of empirical local-measurement frequencies and of empirical averages of commuting single-site observables, with applications to single-site generalized Gibbs ensembles, together with bounds on smooth and spectral entropies.
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BibTeX
@misc{datta2026entropy,
title = {{Entropy Concentration and Universal Typicality for Almost i.i.d. Quantum Sources}},
author = {Nilanjana Datta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.20092},
eprint = {2605.20092},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.20092},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Entropy Concentration and Universal Typicality for Almost i.i.d. Quantum Sources
AU - Nilanjana Datta
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2605.20092
UR - https://arxiv.org/abs/2605.20092
AB - We establish two concentration principles for almost i.i.d. quantum sources under the weakly almost i.i.d. condition, the broadest condition in the established hierarchy of almost i.i.d. sources. Our results therefore apply also to Wasserstein- and Mazzola-Sutter-Renner almost i.i.d. sources. Weakly almost i.i.d. sources are sequences of multipartite states whose fixed-size marginals converge, on average, to tensor powers of a reference state, while allowing arbitrary global correlations and entanglement. We prove a noncommutative weak law of large numbers for empirical observables, and a universal entropy-concentration principle showing asymptotic concentration on subspaces of exponential dimension governed by the von Neumann entropy of the reference state. These concentration principles provide a unified and conceptually transparent approach to several information-theoretic applications beyond the i.i.d. setting, including direct proofs of universal compression within classes of weakly almost i.i.d. sources sharing a common reference state and asymmetric quantum hypothesis-testing bounds. They also yield concentration of empirical local-measurement frequencies and of empirical averages of commuting single-site observables, with applications to single-site generalized Gibbs ensembles, together with bounds on smooth and spectral entropies.
ER -