Related papers: Tsirelson's bound from a Generalised Data Processi…

Local hidden-variable model of singlet-state correlations discussed in M. Czachor, Arithmetic loophole in Bell's Theorem: Overlooked threat to entangled-state quantum cryptography, Acta Phys. Polon. A 139, 70-83 (2021), is shown to be a…

Reversible work extraction from identical quantum systems via collective operations was shown to be possible even without producing entanglement among the sub-parts. Here, we show that implementing such global operations necessarily imply…

It is not generally known, that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of plus and minus 1s that are writable on paper.This surprising fact is not…

A data processing inequality states that the quantity of shared information between two entities (e.g. signals, strings) cannot be significantly increased when one of the entities is processed by certain kinds of transformations. In this…

Change of measure inequalities translate divergences between probability measures into explicit bounds on event probabilities, and play an important role in deriving probabilistic guarantees in learning theory, information theory, and…

Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…

The information convex allows us to look into certain information-theoretic constraints in two-dimensional topological orders. We provide a derivation of the topological contribution $\ln d_a$ to the von Neumann entropy, where $d_a$ is the…

A model of correlated particles described by a generalized probability theory is suggested whose dynamics is subject to a non-linear version of Schr\"odinger equation. Such equations arise in many different contexts, most notably in the…

In a Bell test, the set of observed probability distributions complying with the principle of local realism is fully characterized by Bell inequalities. Quantum theory allows for a violation of these inequalities, which is famously regarded…

We prove number of quantitative stability bounds for the cases of equality in Petz's monotonicity theorem for quasi-relative entropies defined in terms of an operator monotone decreasing functions. Included in our results is a bound in…

We show that classical chaining bounds on the suprema of random processes in terms of entropy numbers can be systematically improved when the underlying set is convex: the entropy numbers need not be computed for the entire set, but only…

Causal parameters may not be point identified in the presence of unobserved confounding. However, information about non-identified parameters, in the form of bounds, may still be recovered from the observed data in some cases. We develop a…

Characterising the capacity region for a network can be extremely difficult, especially when the sources are dependent. Most existing computable outer bounds are relaxations of the Linear Programming bound. One main challenge to extend…

We propose a theoretical understanding of neural networks in terms of Wilsonian effective field theory. The correspondence relies on the fact that many asymptotic neural networks are drawn from Gaussian processes, the analog of…

In the study of quantum nonlocality, one obstacle is that the analytical criterion for identifying the boundaries between quantum and postquantum correlations has not yet been given, even in the simplest Bell scenario. We propose a…

We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…

We give a analytic quantitative relation between Hardy's non-locality and Bell operator. We find that Hardy's non-locality is a sufficient condition for violation of Bell inequality, the upper bound of Hardy's non-locality allowed by…

We prove that a finite correlation length, i.e. exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the…

We study conformal field theories with boundaries, and their boundary renormalization group (RG) flows, using methods from quantum information theory. Positivity of the relative entropy, together with unitarity and Lorentz invariance, give…

We introduce ``local uncertainty relations'' in thermal many-body systems, from which fundamental bounds in quantum systems can be derived. These lead to universal non-relativistic speed limits (independent of interaction range) and…