Related papers: On quantum statistics in data analysis
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
The framework of distributed computing, consisting of several spatially separated input-output servers, has immense importance in distant data manipulation. One of the most challenging parts of this setting is to optimize the use of…
We review some of our recent results (with collaborators) on information processing in an ordered linear spaces framework for probabilistic theories. These include demonstrations that many "inherently quantum" phenomena are in reality quite…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Can the state-space of $d$-dimensional quantum theory be derived from studying the behavior of a single "reference" measuring device? The answer is yes, if the measuring device corresponds to a complex-projective 3-design. In this…
We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to…
Quantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis can not be based on simple Gaussian assumptions. To this extent a method is…
The principle of teleportation can be used to perform a quantum computation even before its quantum input is defined. The basic idea is to perform the quantum computation at some earlier time with qubits which are part of an entangled…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
Planck-scale quantum spacetime undergoes probabilistic local curvature fluctuations whose distributions cannot explicitly depend on position otherwise vacuum's small-scale quantum structure would fail to be statistically homogeneous. Since…
Atomicity is a ubiquitous assumption in distributed computing, under which actions are indivisible and appear sequential. In classical computing, this assumption has several theoretical and practical guarantees. In quantum computing,…
Developing a quantum analog of the modern classical theory of causation, as formulated by Pearl and others using directed acyclic graphs, requires a theory of random or stochastic time development at the microscopic level, where the…
Inspired by Lefschetz thimble theory, we treat Quantum Field Theory as a statistical theory with a complex Probability Distribution Function (PDF). Such complex-valued PDFs permit the violation of Bell-type inequalities, which cannot be…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated paralelly to the the measure theoretic case. It turns out that several classical examples and results have a…
Recently the mathematical formalism of quantum mechanics, especially methods of quantum probability theory, started to be widely used in a variety of applications outside of physics, e.g., cognition and psychology as well as economy and…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…