Related papers: Quantum points/patterns, Part 2. From quantum poin…
We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
Creating quantum algorithms is a difficult task, especially for computer scientist not used to quantum computing. But quantum algorithms often use similar elements. Thus, these elements provide proven solutions to recurring problems, i.e. a…
Gaussian states -- or, more generally, Gaussian operators -- play an important role in Quantum Optics and Quantum Information Science, both in discussions about conceptual issues and in practical applications. We describe, in a tutorial…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
In the framework of deterministic finslerian models, a mechanism producing dissipative dynamics at the Planck scale is discussed. It is based on a geometric evolution from Finsler to Riemann structures defined on the fiber bundle ${ TM}\to…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under…
Macroscopic quantum phenomena refer to quantum features in objects of `large' sizes, systems with many components or degrees of freedom, organized in ways where they can be identified as macroscopic objects. This emerging field is ushered…
Simulating key static and dynamic properties of matter -- from creation in the Big Bang to evolution into sub-atomic and astrophysical environments -- arising from the underlying fundamental quantum fields of the Standard Model and their…
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
Quantum contextual sets have been recognized as resources for universal quantum computation, quantum steering and quantum communication. Therefore, we focus on engineering the sets that support those resources and on determining their…
A general quantum theory encompassing Mechanics, Thermodynamics and irreversible dynamics is presented in two parts. The first part is concerned exclusively with the description of the states of any individual physical system. It is based…
Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite…
Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…