Entropy Concentration and Universal Typicality for Weakly Almost i.i.d. Quantum Sources
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914580605698048 |
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| author | Datta, Nilanjana |
| author_facet | Datta, Nilanjana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20092 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entropy Concentration and Universal Typicality for Weakly Almost i.i.d. Quantum Sources Datta, Nilanjana Quantum Physics 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. |
| title | Entropy Concentration and Universal Typicality for Weakly Almost i.i.d. Quantum Sources |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.20092 |