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Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
We propose a simple abstract formalisation of the act of observation, in which the system and the observer are assumed to be in a pure state and their interaction deterministically changes the states such that the outcome can be read from…
We analyze a quantum measurement where the apparatus is initially in a mixed state. We show that the amount of information gained in a measurement is not equal to the amount of entanglement between the system and the apparatus, but is…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by…
The notion of "closed systems" in Quantum Mechanics is discussed. For this purpose, we study two models of a quantum-mechanical system $P$ spatially far separated from the "rest of the universe" $Q$. Under reasonable assumptions on the…
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain…
The behavior of entangled quantum systems can generally not be explained as being determined by shared classical randomness. In the first part of this paper, we propose a simple game for n players demonstrating this non-local property of…
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
Quantum entanglement describes superposition states in multi-dimensional systems, at least two partite, which cannot be factorized and are thus non-separable. Non-separable states exist also in classical theories involving vector spaces. In…
Classical systems can be entangled. Entanglement is defined by coincidence correlations. Quantum entanglement experiments can be mimicked by a mechanical system with a single conserved variable and 77.8% conditional efficiency. Experiments…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
Effective classicality of a property of a quantum system can be defined using redundancy of its record in the environment. This allows quantum physics to approximate the situation encountered in the classical world: The information about a…
Quantum steering is the phenomenon whereby one party (Alice) proves entanglement by "steering'' the system of another party (Bob) into distinct ensembles of states, by performing different measurements on her subsystem. Here, we investigate…
This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable A and B. In our framework, it…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
We consider different settings of the task to distinguish pure orthogonal quantum states under local operations and a limited amount of classical communication. In the first setting, the spatially separated parties are allowed to perform…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for…