Related papers: On Simplest Kochen-Specker Sets
Kent's conclusion that ``non-contextual hidden variable theories cannot be excluded by theoretical arguments of the Kochen-Specker type once the imprecision in real world experiments is taken into account'' [Phys. Rev. Lett. 83, 3755…
While conversing with chatbots, humans typically tend to ask many questions, a significant portion of which can be answered by referring to large-scale knowledge graphs (KG). While Question Answering (QA) and dialog systems have been…
A perfect strategy is one that allows the mutually in-communicated players of a nonlocal game to win every trial of the game. Perfect strategies are basic tools for some fundamental results in quantum computation and crucial resources for…
Kochen-Specker (KS) theorem lies at the heart of the foundations of quantum mechanics. It establishes impossibility of explaining predictions of quantum theory by any noncontextual ontological model. Spekkens generalized the notion of KS…
Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen-Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been…
The Kochen-Specker theorem proves the inability to assign, simultaneously, noncontextual definite values to all (of a finite set of) quantum mechanical observables in a consistent manner. If one assumes that any definite values behave…
There are contextual sets of multiple qubits whose commutation is parametrized thanks to the coset geometry $\mathcal{G}$ of a subgroup $H$ of the two-generator free group $G=\left\langle x,y\right\rangle$. One defines geometric…
Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the {\em kernel} of the program, is…
Using a graph approach to quantum systems, we prove that descriptions of 3-dim Kochen-Specker (KS) setups as well as descriptions of 3-dim spin systems by means of Greechie lattices that we find in the literature are wrong. Correct lattices…
A set $P = H \cup \{w\}$ of $n+1$ points in general position in the plane is called a wheel set if all points but $w$ are extreme. We show that for the purpose of counting crossing-free geometric graphs on such a set $P$, it suffices to…
In this paper we present the first model for directly synthesizing fluent, natural-sounding spoken audio captions for images that does not require natural language text as an intermediate representation or source of supervision. Instead, we…
In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. We will argue that there exists a general confusion within the foundational literature arising from the improper "scrambling" of two…
Physical entities are ultimately (re)constructed from elementary yes/no events, in particular clicks in detectors or measurement devices recording quanta. Recently, the interpretation of certain such clicks has given rise to unfounded…
A generalized Kochen-Specker theorem is proved. It is shown that there exist sets of $n$ projection operators, representing $n$ yes-no questions about a quantum system, such that none of the $2^n$ possible answers is compatible with sum…
We introduce a notion of contextuality for transformations in sequential contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of contextuality. Within a transformation-based model for quantum computation we show that strong…
We describe a phase-adjusted realification procedure that embeds any finite set of rays in C^3 into R^3. By assigning an appropriate phase to each ray before applying the standard coordinate-wise map, we can arrange that two rays are…
Sphere-bases are constructed for the $\mathbb{Z}_2$ vector space formed by the $k$-dimensional subcomplexes, of $n$-simplex (or $n$-cube), for which every $(k{-}1)$-face is contained in a positive even number of $k$-cells; addition is…
How many words are needed to define all the words in a dictionary? Graph-theoretic analysis reveals that about 10% of a dictionary is a unique Kernel of words that define one another and all the rest, but this is not the smallest such…
Generating coherent and useful image/video scenes from a free-form textual description is technically a very difficult problem to handle. Textual description of the same scene can vary greatly from person to person, or sometimes even for…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…