Almost-iid information theory

TL;DR

This paper investigates whether almost-iid quantum states can serve as effective substitutes for iid states in information theory, demonstrating that key entropy measures and entanglement properties are asymptotically equivalent.

Contribution

It proves that the conditional entropy of almost-iid states converges to that of iid states, showing robustness of entanglement measures like squashed entanglement.

Findings

Conditional entropy of almost-iid states matches iid states asymptotically

Squashed entanglement is robust for almost-iid states

Operationally motivated symmetry assumptions lead to almost-iid descriptions

Abstract

Information-theoretic techniques are based on the assumption that resources are well characterized by independent and identically distributed (iid) states. This assumption cannot be justified operationally, since, for example, correlations between subsequent systems emitted by a source cannot be detected by any practical tomographic protocol. Operationally motivated symmetry assumptions still imply, via de Finetti theorems, that the resources are described by almost-iid states. This raises the question: Are almost-iid resources as effective as perfect iid resources for information-processing tasks? Here we address this question and prove that the conditional entropy of almost-iid states asymptotically coincides with that of iid states. As an application, this implies that squashed entanglement is robust for almost-iid states, asymptotically matching its value on iid states.