Related papers: Testing quantum theory by generalizing noncontextu…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a…
The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker…
Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified on various physical systems.…
Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well.…
We propose two quantum experiments - modified Bell tests - that could detect contextual hidden variables underlying quantum mechanics. The experiments are inspired by hydrodynamic pilot-wave systems that mimic a wide range of quantum…
I propose a general quantum hypothesis testing theory that enables one to test hypotheses about any aspect of a physical system, including its dynamics, based on a series of observations. For example, the hypotheses can be about the…
Bell's theorem guarantees that no model based on local variables can reproduce quantum correlations. Also some models based on non-local variables, if subject to apparently "reasonable" constraints, may fail to reproduce quantum physics. In…
Kirkwood-Dirac representations of quantum states are increasingly finding use in many areas within quantum theory. Usually, representations of this sort are only applied to provide a representation of quantum states (as complex functions…
In this letter, we propose and experimentally test a quantumness criterion for single systems. The criterion is based on the violation of an already reported classical inequality. This inequality is expressed in terms of joint probabilities…
The framework of generalized probabilistic theories (GPT) is a widely-used approach for studying the physical foundations of quantum theory. The standard GPT framework assumes the no-restriction hypothesis, in which the state space of a…
A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional…
A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory.…
Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…
In order to find a physical axiomatization of quantum theory, physical theories are often considered as a special case of a much more general framework of generalized probabilistic theories. We first present a detailed introduction to…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A…
A different approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible to assign numerical…
Starting from arbitrary sets of quantum states and measurements, referred to as the prepare-and-measure scenario, an operationally noncontextual ontological model of the quantum statistics associated with the prepare-and-measure scenario is…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…