New approaches to almost i.i.d. information theory
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918501800738816 |
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| author | Girardi, Filippo De Palma, Giacomo Lami, Ludovico |
| author_facet | Girardi, Filippo De Palma, Giacomo Lami, Ludovico |
| contents | Independent and identically distributed (i.i.d.) states are ubiquitous in quantum information theory. However, in a practical setting, the i.i.d. assumption is too stringent, and possibly not realistic. A physically more compelling class of 'almost i.i.d.' sources was recently proposed by [Mazzola/Sutter/Renner, arXiv:2603.15792]. In this paper, we introduce two alternative definitions of almost i.i.d. states, based on the normalised quantum Wasserstein distance and on the idea of looking at the average $k$-body marginal. We explore some basic properties of these notions and prove a strict hierarchical relation among them, with Mazzola et al.'s notion being the strictest, the one based on $k$-body marginals the loosest, and the one based on the quantum Wasserstein distance in between. Strict separation is established by means of explicit examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15114 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | New approaches to almost i.i.d. information theory Girardi, Filippo De Palma, Giacomo Lami, Ludovico Quantum Physics Mathematical Physics Independent and identically distributed (i.i.d.) states are ubiquitous in quantum information theory. However, in a practical setting, the i.i.d. assumption is too stringent, and possibly not realistic. A physically more compelling class of 'almost i.i.d.' sources was recently proposed by [Mazzola/Sutter/Renner, arXiv:2603.15792]. In this paper, we introduce two alternative definitions of almost i.i.d. states, based on the normalised quantum Wasserstein distance and on the idea of looking at the average $k$-body marginal. We explore some basic properties of these notions and prove a strict hierarchical relation among them, with Mazzola et al.'s notion being the strictest, the one based on $k$-body marginals the loosest, and the one based on the quantum Wasserstein distance in between. Strict separation is established by means of explicit examples. |
| title | New approaches to almost i.i.d. information theory |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2605.15114 |