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Magneto-optical effect is a fundamental but broad concept in magnetic mediums. Here we propose a scheme for its quantum emulation using ultracold atoms. By representing the light-medium interaction in the quantum-emulation manner, the…

Observables have a dual nature in both classical and quantum kinematics: they are at the same time \emph{quantities}, allowing to separate states by means of their numerical values, and \emph{generators of transformations}, establishing…

We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…

In quantum mechanics, the measureable quantities of a given theory are predicted by performing a weighted sum over possibilities. We show how to arrange the possibilities into bundles such that the associated subsums can be viewed as…

A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…

Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…

It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…

We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In…

In the current debate referring to the construction of a tenable background independent theory of Quantum Gravity we introduce the notion of topos-theoretic relativization of physical representability and demonstrate its relevance…

The theory of decoherence attempts to explain the emergent classical behaviour of a quantum system interacting with its quantum environment. In order to formalize this mechanism we introduce the idea that the information preserved in an…

We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann…

Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…

In Quantum Physics there are circumstances where the direct measurement of particular observables encounters diffculties; in some of these cases, however, its value can be evaluated, i.e. it can be inferred by measuring another observable…

Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in…

Observables in quantum gravity are famously defined asymptotically, at the boundary of AdS or Minkowski spaces. However, by gauge fixing a coordinate system or suitably dressing the field operators, an approximate, "quasi-local" approach is…

In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…

We introduce a new concept, `(topological) (vacuum) parallel world, ' which is a new tool to research submanifolds. Roughly speaking, `Observables in (T)QFT' is equal to `a (topological) modification of space-time.' In other words, we give…

We demonstrate that temporal observables, which are sensitive to a system's history (as opposed to its state), implicate entangled histories. We exemplify protocols for measuring such observables, and algorithms for predicting the…

Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…

We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…