Related papers: Nonlinear probability. A theory with incompatible …
An extension of the Born rule, the {\it quantum typicality rule}, has recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into…
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…
Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
Quantum mechanics notoriously faces the measurement problem, the problem that if read thoroughly, it implies the nonexistence of definite outcomes in measurement procedures. A plausible reaction to this and to related problems is to regard…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
Masanes, Galley and M\"uller [1] argue that the measurement postulates of non-relativistic quantum mechanics follow from the structural postulates together with an assumption they call the "possibility of state estimation". Their argument…
We discuss the (re-)construction of quasiprobability representations from generic measurements, including noisy ones. Based on the measurement under study, quasiprobabilities and the associated concept of nonclassicality are introduced. A…
It is shown that in two-state quantum theory, a generic quantum state can be described by a non-computable real number. In terms of this, the criterion for measurement outcome is simply and deterministically defined. This demonstration is…
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we…
Many situations in quantum theory and other areas of physics lead to quasi-probabilities which seem to be physically useful but can be negative. The interpretation of such objects is not at all clear. In this paper, we show that…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
Measurement incompatibility is a distinguishing property of quantum physics and an essential resource for many quantum information processing tasks. We introduce an approach to verify the joint measurability of measurements based on…
Majorization theory is a powerful mathematical tool to compare the disorder in distributions, with wide-ranging applications in many fields including mathematics, physics, information theory, and economics. While majorization theory…
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
Nies and Scholz introduced the notion of a state to describe an infinite sequence of qubits and defined quantum-Martin-Lof randomness for states, analogously to the well known concept of Martin-L\"of randomness for elements of Cantor space…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…