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

• URL: http://arxiv.org/abs/2605.15114v1
• Date: Thu, 14 May 2026 17:27:47 GMT
• Title: New approaches to almost i.i.d. information theory
• Abstract summary: Independent and identically distributed (i.i.d.) states are ubiquitous in quantum information theory.<n>A physically more compelling class of 'almost i.i.d.' sources was recently proposed by [Mazzola/Sutter/Renner, arXiv:2603.15792]<n>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.
• Score: 12.93569110166645
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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