Entropic uncertainty relations for quantum information scrambling

TL;DR

This paper establishes entropic uncertainty relations for quantum information scrambling, linking measures of operator incompatibility with the spread of quantum information, and demonstrates their implications through numerical simulations and experimental relevance.

Contribution

It unifies entropic uncertainty relations with quantum scrambling, introducing bounds that incorporate quasiprobabilities and weak measurements, revealing new physical insights.

Findings

Scrambling strengthens entropic uncertainty bounds in spin chain simulations.

Weak measurements and quasiprobabilities are key to the uncertainty relations.

The results connect operator incompatibility with information spreading in quantum systems.

Abstract

How violently do two quantum operators disagree? Different fields of physics feature different measures of incompatibility: (i) In quantum information theory, entropic uncertainty relations constrain measurement outcomes. (ii) In condensed matter and high-energy physics, the out-of-time-ordered correlator (OTOC) signals scrambling, the spread of information through many-body entanglement. We unite these measures, proving entropic uncertainty relations for scrambling. The entropies are of distributions over weak and strong measurements' possible outcomes. The weak measurements ensure that the OTOC quasiprobability (a nonclassical generalization of a probability, which coarse-grains to the OTOC) governs terms in the uncertainty bound. The quasiprobability causes scrambling to strengthen the bound in numerical simulations of a spin chain. This strengthening shows that entropic uncertainty relations can reflect the type of operator disagreement behind scrambling. Generalizing beyond scrambling, we prove entropic uncertainty relations satisfied by commonly performed weak-measurement experiments. We unveil a physical significance of weak values (conditioned expectation values): as governing terms in entropic uncertainty bounds.