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We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given…

For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…

It is shown that the statistical conception of quantum mechanics is dynamical but not probabilistic, i.e. the statistical description in quantum mechanics is founded on dynamics. A use of the probability theory, when it takes place, is…

Quantum mechanics led to spectacular technological developments, discovery of new constituents of matter and new materials. However there is still no consensus on its interpretation and limitations. Some scientists and scientific writers…

Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…

Quantum theory encounters a difficulty when attempting to describe recording devices. If the recording is of events in which quantum uncertainty plays a role, such as an experiment on a quantum system, quantum theory is unable to correctly…

A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…

Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…

Why does such a successful theory like Quantum Mechanics have so many mysteries? The history of this theory is replete with dubious interpretations and controversies, and yet a knowledge of its predictions, however, contributed to the…

Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is…

Quantum uncertainty is described here in two guises: indeterminacy with its concomitant indeterminism of measurement outcomes, and fuzziness, or unsharpness. Both features were long seen as obstructions of experimental possibilities that…

Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…

Quantum Mechanics, the physical theory describing the microworld, represents one of science's greatest triumphs. It lies at the root of all modern digital technologies and offers unparalleled correspondence between prediction and…

The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and…

Proofs of the security of quantum key distribution are propositions about models written in the mathematical language of quantum mechanics, and the issue is the linking of such models to actual devices in an experiment on security. To…

We provide a reinterpretation of the quantum vacuum ambiguities that one encounters when studying particle creation phenomena due to an external and time-dependent agent. We propose a measurement-motivated understanding: Each way of…

An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…

Quantum uncertainty is a well-known property of quantum mechanics that states the impossibility of predicting measurement outcomes of multiple incompatible observables simultaneously. In contrast, the uncertainty in the classical domain…

The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing…

Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…