Related papers: A Topos Perspective on the Kochen-Specker Theorem:…
All simple translation-invariant valuations on polytopes are classified. As a direct consequence the well-known conditions for translative-equidecomposability are recovered. Furthermore, a simplified proof of the classification of…
In the paper it is argued that the Kochen-Specker theorem necessitates a conclusion that for a quantum system it is possible to find a set of projection operators which is not truth-value bivalent; that is, a bivalent truth-value assignment…
Quantum contextuality takes an important place amongst the concepts of quantum computing that bring an advantage over its classical counterpart. For a large class of contextuality proofs, aka. observable-based proofs of the Kochen-Specker…
Contextuality is a key feature of quantum mechanics, as was first brought to light by Bohr and later realised more technically by Kochen and Specker. Isham and Butterfield put contextuality at the heart of their topos-based formalism and…
Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…
In this paper we present different ways to parametrize subsets of the space of valuations on $K[x]$ extending a given valuation on $K$. We discuss the methods using pseudo-Cauchy sequences and approximation types. The method presented here…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
By the example of the proof of Minkowski's conjecture on critical determinant we give a category theory framework for interval computation.
We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to…
Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the…
An original entity is defined to study quantum beams of conserved particles. The beam is described as a Stationary Incoherent Superposition of Wave packets (SISOW). Mean values are time-independent confirming that the SISOW describes a…
The aim of this paper is to build a theory of commutative and noncommutative {\it injective} valuations of various algebras (including algebras with zero divisors). The targets of our valuations are (well-)ordered commutative and…
A different approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible to assign numerical…
We study essentially bounded quantum random variables and show that the Gelfand spectrum of such a quantum random variable coincides with the hypoconvex hull of its essential range. Moreover, a notion of operator-valued variance is…
We extend the classical forbidden-interval theorems for a stochastic-resonance noise benefit in a nonlinear system to a quantum-optical communication model and a continuous-variable quantum key distribution model. Each quantum…
Value-of-information analyses provide a straightforward means for selecting the best next observation to make, and for determining whether it is better to gather additional information or to act immediately. Determining the next best test…
In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic…
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…
In this paper we attempt to discuss what has Kochen-Specker (KS) theorem to say about physical invariance and quantum individuality. In particular, we will discuss the impossibility of making reference to objective physical properties…
The Kochen-Specker Theorem is widely interpreted to imply that non-contextual hidden variable theories that agree with the predictions of Copenhagen quantum mechanics are impossible. The import of the theorem for a novel observer…