Related papers: Bell's inequalities in the tomographic representat…
Quantum tomography is a method to experimentally extract all that is observable about a quantum mechanical system. We introduce quantum tomography to collider physics with the illustration of the angular distribution of lepton pairs. The…
The assumptions required for the derivation of Bell inequalities are not usually satisfied for random fields in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical…
Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto probability distribution of discrete random variables (spin projections). The operators acting on the fermion states are…
Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum…
Bell inequalities constitute a key tool in quantum information theory: they not only allow one to reveal nonlocality in composite quantum systems, but, more importantly, they can be used to certify relevant properties thereof. We provide a…
The probability representation for quantum states of the universe in which the states are described by a fair probability distribution instead of wave function (or density matrix) is developed to consider cosmological dynamics. The…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…
Stochastic and bistochastic matrices providing positive maps for spin states (for qudits) are shown to form semigroups with dense intersection with the Lie groups $IGL(n, \mathbb{R})$ and $GL(n, \mathbb{R})$ respectively. The density matrix…
Given a sequence of pairs of spin-one half particles in the singlet state, assume that Alice measures the normalized projections along some vector of the spins of one vector per pair along that vector while Bob measures the normalized…
Tomograms introduced for the description of quantum states in terms of probability distributions are shown to be related to a standard star-product quantization with appropriate kernels. Examples of symplectic tomograms and spin tomograms…
Initially motivated by their relevance in foundations of quantum mechanics and more recently by their applications in different contexts of quantum information science, violations of Bell inequalities have been extensively studied during…
We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is quantum-like. There is presented the scheme for an…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
Standard tomographic analyses ignore model uncertainty. It is assumed that a given model generated the data and the task is to estimate the quantum state, or a subset of parameters within that model. Here we apply a model averaging…
Both the quantum mechanical and classical Bells experiment are within the focus of this paper. The fact that one measures different probabilities in both experiments is traced back to the superposition of two orthogonal but nonentangled…
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…
We describe quantum tomography as an inverse statistical problem and show how entropy methods can be used to study the behaviour of sieved maximum likelihood estimators. There remain many open problems, and a main purpose of the paper is to…
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…