Related papers: Nonlinear probability. A theory with incompatible …
Density matrices are the most general descriptions of quantum states, covering both pure and mixed states. Positive semidefiniteness is a physical requirement of density matrices, imposing nonnegative probabilities of measuring physical…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
Peng (2006) initiated a new kind of central limit theorem under sub-linear expectations. Song (2017) gave an estimate of the rate of convergence of Peng's central limit theorem. Based on these results, we establish a new kind of almost sure…
Quasi-probabilities appear across diverse areas of physics, but their conceptual foundations remain unclear: they are often treated merely as computational tools, and operations like conditioning and Bayes' theorem become ambiguous. We…
This paper introduces a novel quasi-likelihood extension of the generalised Kendall \(\tau_{a}\) estimator, together with an extension of the Kemeny metric and its associated covariance and correlation forms. The central contribution is to…
In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can…
It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, that is that its integral is one and that the marginal properties are satisfied.…
We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
The notion of measurements is central for many debates in quantum mechanics. One critical point is whether a measurement can be regarded as an absolute event, giving the same result for any observer in an irreversible manner. Using ideas…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
This article reviews six historically important papers in the development of the theory of measurement for nonlocal variables in quantum mechanics, with special emphasis the non violation of relativistic causality. Spanning more than…
Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…
In any probabilistic theory, we may say a bipartite state on a composite system AB steers its marginal state (on, say, system B) if, for any decomposition of the marginal as a mixture, with probabilities p_i, of states b_i of B, there…
A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the…
We address the issue of coupling variables which are essentially classical to variables that are quantum. Two approaches are discussed. In the first (based on collaborative work with L.Di\'osi), continuous quantum measurement theory is used…
In prior work, we have shown how the basic concepts and terms of quantum mechanics relate to factorizations and marginals of complex-valued quantum mass functions, which are generalizations of joint probability mass functions. In this…
Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many…
We propose a theory of quantum (statistical) measurement which is close, in spirit, to Hepp's theory, which is centered on the concepts of decoherence and macroscopic (classical) observables, and apply it to a model of the Stern-Gerlach…