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

• URL: http://arxiv.org/abs/2605.20092v1
• Date: Tue, 19 May 2026 16:48:03 GMT
• Title: Entropy Concentration and Universal Typicality for Weakly Almost i.i.d. Quantum Sources
• Abstract summary: Weakly almost i.i.d. quantum sources are sequences of multipartite states whose fixed-size marginals converge to tensor powers of a reference state.<n>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 concentration on subspaces of exponential dimension governed by the von Neumann entropy of the reference state.
• Score: 11.844977816228043
• License: http://creativecommons.org/licenses/by/4.0/
• 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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