Related papers: Tsirelson's bound from a Generalised Data Processi…
The Bell-Clauser-Horne-Shimony-Holt inequality can be used to show that no local hidden-variable theory can reproduce the correlations predicted by quantum mechanics (QM). It can be proved that certain QM correlations lead to a violation of…
The principle called information causality has been used to deduce Tsirelson's bound. In this paper we derive information causality from monotonicity of divergence and relate it to more basic principles related to measurements on…
We consider the problem of distinguishing between a set of arbitrary quantum states in a setting in which the time available to perform the measurement is limited. We provide simple upper bounds on how well we can perform state…
We present a non-linear inequality that completely characterizes the set of correlation functions obtained from bipartite quantum systems, for the case in which measurements on each subsystem can be chosen between two arbitrary dichotomic…
A physical explanation for quantum bounds to nonlocality (Tsirelson's bound) is a fundamental problem that remains open, and one approach to explaining its origins is the so-called Exclusivity principle, relying on probabilistic assumptions…
The idea that non-local correlations stronger than quantum correlations between two no-signaling systems could theoretically exist is based on an incorrect statistical interpretation of the no-signaling condition. This article shows that…
In this work, we study the generalization capability of algorithms from an information-theoretic perspective. It has been shown that the expected generalization error of an algorithm is bounded from above by a function of the relative…
Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of correlations as quantum theory in every causal structure.…
We show a relation between entanglement and correlations of any form. The internal entanglement of a bipartite system, and its correlations with another system, limit each other. A measure of correlations, of any nature, cannot increase…
Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
We analyze a family of measures of general quantum correlations for composite systems, defined in terms of the bipartite entanglement necessarily created between systems and apparatuses during local measurements. For every entanglement…
The existence of a global causal order between events places constraints on the correlations that parties may share. Such "causal correlations" have been the focus of recent attention, driven by the realization that some extensions of…
We describe a new technique for obtaining Tsirelson bounds, or upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signaling, we obtain a Tsirelson bound by maximizing over all no-signaling…
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…
The first part of this paper contains an introduction to Bell inequalities and Tsirelson's theorem for the non-specialist. The next part gives an explicit optimum construction for the "hard" part of Tsirelson's theorem. In the final part we…
Superquantum ("PR-box") correlations, though designed to respect relativistic causality, violate relativistic causality in the classical limit. Generalizing to all stronger-than-quantum bipartite correlations, I derive Tsirelson's bound…
A quantum network consists of independent sources distributing entangled states to distant nodes which can then perform entangled measurements, thus establishing correlations across the entire network. But how strong can these correlations…
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…
Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that…