Informationally restricted quantum correlations

TL;DR

This paper investigates quantum correlations in prepare-and-measure scenarios under an information bound, revealing that limiting information yields stronger quantum correlations than dimension constraints and providing device-independent tests.

Contribution

It introduces a novel framework focusing on information bounds instead of dimension, characterizes classical correlations, and demonstrates the strength of quantum communication with information constraints.

Findings

Quantum correlations surpass classical ones under information bounds.

Limiting information leads to stronger quantum correlations than limiting dimension.

Device-independent tests can estimate the information content from observed correlations.

Abstract

Quantum communication leads to strong correlations, that can outperform classical ones. Complementary to previous works in this area, we investigate correlations in prepare-and-measure scenarios assuming a bound on the information content of the quantum communication, rather than on its Hilbert-space dimension. Specifically, we explore the extent of classical and quantum correlations given an upper bound on the one-shot accessible information. We provide a characterisation of the set of classical correlations and show that quantum correlations are stronger than classical ones. We also show that limiting information rather than dimension leads to stronger quantum correlations. Moreover, we present device-independent tests for placing lower bounds on the information given observed correlations. Finally, we show that quantum communication carrying $\log d$ bits of information is at least as strong a resource as $d$-dimensional classical communication assisted by pre-shared entanglement.