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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.
We provide a protocol to measure out-of-time-order correlation functions. These correlation functions are of theoretical interest for diagnosing the scrambling of quantum information in black holes and strongly interacting quantum systems generally.
Interaction in quantum systems can spread initially localized quantum information into the many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is the key to resolving various conundrums in physics. H
Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we review recent r
We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two {distinctive operational} scenarios. In the first scenario, by merging {two successive measurements} into
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen through the