Finally, the chapter on measurements could have been extended by a brief discussion of the infamous measurement problem of quantum physics. To summarise, the authors present a thorough and well-structured treatise on the mathematical language of quantum theory. I can recommend it to any graduate ...
The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement This book presents a clear and detailed exposition of the fundamental concepts of quantum theory: states, effects, observables, channels and instruments. It introduces several up-to-date topics, such as state discrimination,...
This was first achieved by quantum theory. We shall therefore go into the theory in more depth, beginning where Chap. 7 left off. We shall be particularly, but not exclusively, concerned with bound states, of which the simpest example is...
Quantum PhysicsThe mathematical formalism of quantum theory has been successfully used in human cognition to model decision processes and to deliver representations of human knowledge. As such, quantum cognition inspired tools have improved technologies for Natural Language Processing and Information Retrieval...
(Atomic Physics) a theory concerning the behaviour of physical systems based on Planck's idea that they can only possess certain properties, such as energy and angular momentum, in discrete amounts (quanta). The theory later developed in several equivalent mathematical forms based on De Broglie'...
The mathematical abstraction of an RC can generally be described in the language of dynamical systems, as follows. Consider a coupled system of equations $$\left\{\begin{array}{l}\Delta {{{ x}}}=F({{{ x}}};{{{ u}}};{{{ p}}}),\quad \\ {{{ y}}}=G({{{ x}}};{{{ ...
Archive for Mathematical Logic20 July 2024 Intuitionistic sets and numbers: small set theory and Heyting arithmetic Archive for Mathematical Logic18 June 2024 The Tarski–Lindenbaum algebra of the class of strongly constructivizable models with $$omega $$ -stable theories ...
When you and I talk, you and I are bilingual, we think about what we’re going to say, and it’s relatively independent of the language in which we’re going to say. When we talk about, I don’t know, let’s say a mathematical concept or something, the kind of thinking that we...
Another possibility is that our understanding of computation in possible physical theories is couched too much in the language of quantum theory. For example, it could be entirely possible to have a theory that has the same computational power as quantum theory but barely resembles it. We thus ...
The first steps will thus be to translate the Axioms into mathematical constraints on probabilities relating modalities. This will lead us to manipulate N× N probability matrices, in a general way not restricted to the quantum formalism. Using our Axioms to obtain physically-based constraints, we...