Learning properties of quantum states without the IID assumption.

We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.

Certified algorithms for equilibrium states of local quantum Hamiltonians.

Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to result in undecidable problems. Using a finite-size scaling of algorithms devised for finite systems often fails due to the lack of certified convergence bounds for this limit.

Mathematical discoveries from program search with large language models.

Large language models (LLMs) have demonstrated tremendous capabilities in solving complex tasks, from quantitative reasoning to understanding natural language. However, LLMs sometimes suffer from confabulations (or hallucinations), which can result in them making plausible but incorrect statements. This hinders the use of current large models in scientific discovery.

Metabolomic profiling of bacterial biofilm: trends, challenges, and an emerging antibiofilm target.

Biofilm-related infections substantially contribute to bacterial illnesses, with estimates indicating that at least 80% of such diseases are linked to biofilms. Biofilms exhibit unique metabolic patterns that set them apart from their planktonic counterparts, resulting in significant metabolic reprogramming during biofilm formation. Differential glycolytic enzymes suggest that central metabolic processes are markedly different in biofilms and planktonic cells.

Computing conditional entropies for quantum correlations.

The rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum states jointly held by the adversary and the parties that are consistent with the statistics that are seen by the parties. Here, we introduce a method to approximate such entropic quantities.

Chain Rule for the Quantum Relative Entropy.

The chain rule for the classical relative entropy ensures that the relative entropy between probability distributions on multipartite systems can be decomposed into a sum of relative entropies of suitably chosen conditional distributions on the individual systems. Here, we prove a chain rule inequality for the quantum relative entropy. The new chain rule allows us to solve an open problem in the context of asymptotic quantum channel discrimination: surprisingly, adaptive protocols cannot improve the error rate for asymmetric channel discrimination compared to nonadaptive strategies.

Practical device-independent quantum cryptography via entropy accumulation.

Device-independent cryptography goes beyond conventional quantum cryptography by providing security that holds independently of the quality of the underlying physical devices. Device-independent protocols are based on the quantum phenomena of non-locality and the violation of Bell inequalities. This high level of security could so far only be established under conditions which are not achievable experimentally.

Universal recovery map for approximate Markov chains.

A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that the measures the performance of such recovery operations.