New approaches to almost i.i.d. information theory

Title:New approaches to almost i.i.d. information theory

Abstract: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.

25 pages, 1 figure. Sections 3.4 and 3.5 are new

arXiv:2605.15114 [quant-ph]

(or arXiv:2605.15114v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.15114 Focus to learn more arXiv-issued DOI via DataCite

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