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arXiv · 2605.20092

Entropy Concentration and Universal Typicality for Weakly Almost i.i.d. Quantum Sources

Nilanjana Datta
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Abstract

Weakly almost i.i.d. quantum 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 establish two concentration principles for such sources: 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, asymmetric quantum hypothesis-testing bounds, concentration results for macroscopic observables in quantum many-body systems including generalized Gibbs ensembles and for repeated local measurement statistics, as well as bounds on smooth- and spectral entropy quantities.

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Nilanjana Datta. 2026-05-19. Entropy Concentration and Universal Typicality for Weakly Almost i.i.d. Quantum Sources. https://arxiv.org/abs/2605.20092

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