Related papers: Beyond real: Investigating the role of complex num…
Bell inequality with self-testing property has played an important role in quantum information field with both fundamental and practical applications. However, it is generally challenging to find Bell inequalities with self-testing property…
The necessity of complex numbers in quantum mechanics has long been debated. This paper develops a real Kahler space formulation of quantum mechanics [19], asserting equivalence to the standard complex Hilbert space framework. By mapping…
Tests of Bell's theorem rule out local hidden variables theories. But any theorem is only as good as the assumptions that go into it, and one of these assumptions is that the experimenter can freely chose the detector settings. Without this…
Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there…
The no-signalling principle is a fundamental assumption in Bell-inequality and quantum-steering experiments. Nonetheless, experimental imperfections can lead to apparent violations beyond those expected from finite-sample statistics. Here,…
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…
Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently…
We define and study a new notion of "robust simulations" between complexity classes which is intermediate between the traditional notions of infinitely-often and almost-everywhere, as well as a corresponding notion of "significant…
It has been known that all bipartite pure quantum states can be certified by quantum self-testing, i.e., any such states can be pinned down completely based on the statistics produced by local quantum measurements. A notable feature of…
Genetic data are frequently categorical and have complex dependence structures that are not always well understood. For this reason, clustering and classification based on genetic data, while highly relevant, are challenging statistical…
We derive a multipartite generalized Bell inequality which involves the entire range of settings for each of the local observers. Especially, it is applied to show non-local behavior of a six-qubit mixture of Greenberger-Horne-Zeilinger…
Computer-based modelling and simulation have become useful tools to facilitate humans to understand systems in different domains, such as physics, astrophysics, chemistry, biology, economics, engineering and social science. A complex system…
The celebrated Einstein-Podolsky-Rosen quantum steering has a complex structure in the multipartite scenario. We show that a naively defined criterion for multipartite steering allows, like in Bell nonlocality, for a contradictory effect…
Complex-valued data is ubiquitous in signal and image processing applications, and complex-valued representations in deep learning have appealing theoretical properties. While these aspects have long been recognized, complex-valued deep…
Measurements performed on distant parts of an entangled quantum state can generate correlations incompatible with classical theories respecting the assumption of local causality. This is the phenomenon known as quantum non-locality that,…
Bell non-locality is a powerful framework to distinguish classical, quantum and post-quantum resources, which relies on non-communicating players. Under which restriction can we have the same separations, if we allow for communication?…
Non-locality stands nowadays not only as one of the cornerstones of quantum theory, but also plays a crucial role in quantum information processing. Several experimental investigations of nonlocality have been carried out over the years. In…
Bell's test, initially devised to distinguish quantum theory from local hidden variable models through {violations of local bounds}, is also a common tool for detecting entanglement. For this purpose, one can assume the quantum description…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…
Quantum theory allows for nonlocality without entanglement. Notably, there exist bipartite quantum measurements consisting of only product eigenstates, yet they cannot be implemented via local quantum operations and classical communication.…