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We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
Euclidean volume ratios between quantum states with positive partial transpose and all quantum states in bipartite systems are investigated. These ratios allow a quantitative exploration of the typicality of entanglement and of its…
Many typical Bell experiments can be described as follows. A source repeatedly distributes particles among two spacelike separated observers. Each of them makes a measurement, using an observable randomly chosen out of several possible…
The precision with which we can measure operators that do not commute with conserved quantities is limited by the need to preserve the associated global symmetries. We show how to construct a local hidden-variable model that violates Bell…
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…
Based on the new general framework for the probabilistic description of experiments, introduced in quant-ph/0305126, quant-ph/0312199, we analyze in mathematical terms the link between the validity of Bell-type inequalities under joint…
Simulating key static and dynamic properties of matter -- from creation in the Big Bang to evolution into sub-atomic and astrophysical environments -- arising from the underlying fundamental quantum fields of the Standard Model and their…
The quantum mechanical measurement process is considered. A hypothetical concept of irrational dynamical variables is proposed. A possible definition of measurement is discussed along with a mathematical method to calculate experimental…
A model for two entangled systems in an EPR setting is shown to reproduce the quantum-mechanical outcomes and expectation values. Each system is represented by a small sphere containing a point-like particle embedded in a field. A quantum…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
Bell inequalities are mathematical constructs that demarcate the boundary between quantum and classical physics. A new class of multiplicative Bell inequalities originating from a volume maximization game (based on products of correlators…
The empirical proof of Bell inequality violations was a landmark moment for research into quantum foundations. It commits us to a universe without strict relativistic locality or requires that we escape through a potential loophole like…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
We demonstrate a complete, probabilistic quantum dynamical simulation of the standard nonlinear Hamiltonian of optomechanics, including decoherence at finite temperatures. Robust entanglement of an optical pulse with the oscillator is…
We demonstrate that the EPR-Bohm probabilities can be easily obtained in the classical (but contextual) probabilistic framework by using the formula of interference of probabilities. From this point of view the EPR-Bell experiment is just…
We present educational material about Bell inequalities in the context of quantum computing. In particular, we provide software tools to simulate their violation, together with a guide for the classroom discussion. The material is organized…
The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell violation measurement is performed. From an observer in the laboratory frame, a Bell violation is…
Quantum mechanics challenges our intuition on the cause-effect relations in nature. Some fundamental concepts, including Reichenbach's common cause principle or the notion of local realism, have to be reconsidered. Traditionally, this is…
We report the measurement of a Bell inequality violation with a single atom and a single photon prepared in a probabilistic entangled state. This is the first demonstration of such a violation with particles of different species. The…