Related papers: On Simplest Kochen-Specker Sets
Semantic knowledge can be a great asset to natural language processing systems, but it is usually hand-coded for each application. Although some semantic information is available in general-purpose knowledge bases such as WordNet and Cyc,…
Virtually all of the analysis of quantum contextuality is restricted to the case where events are represented by rank-one projectors. This restriction is arbitrary and not motivated by physical considerations. We show here that loosening…
Quantum systems show contextuality. More precisely, it is impossible to reproduce the quantum-mechanical predictions using a non-contextual realist model, i.e., a model where the outcome of one measurement is independent of the choice of…
A sememe is defined as the minimum semantic unit of human languages. Sememe knowledge bases (KBs), which contain words annotated with sememes, have been successfully applied to many NLP tasks, and we believe that by learning the smallest…
It is pointed out that the 60 complex rays in four dimensions associated with a system of two qubits yield over 10^9 critical parity proofs of the Kochen-Specker theorem. The geometrical properties of the rays are described, an overview of…
Quantum mechanics implies that not all physical properties can be simultaneously well defined, such as the momentum and position due to Heisenberg uncertainty principle. Some alternative theories have been explored, notably the…
Randomness is a potential resource for cryptography, simulations and algorithms. Non-local correlations violating Bell's inequality certify the generation of bit strings whose randomness is guaranteed in a device-independent manner. We…
In the age of information abundance, the ability to provide users with contextually relevant and concise information is crucial. Keyword in Context (KIC) generation is a task that plays a vital role in and generation applications, such as…
The Kochen-Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind of hidden states models. In this paper, we…
All quantum random number generators based on measuring value indefinite observables are at least three-dimensional because the Kochen-Specker Theorem and the Located Kochen-Specker Theorem are false in dimension two. In this article, we…
Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations…
The Kochen-Specker theorem shows that it is impossible to assign sharp values to all dynamical variables in quantum mechanics in such a way that the algebraic relations among the values of dynamical variables whose self-adjoint operators…
Vision-based Semantic Scene Completion (SSC) has gained much attention due to its widespread applications in various 3D perception tasks. Existing sparse-to-dense approaches typically employ shared context-independent queries across various…
The Kochen-Specker no-go theorem established that hidden-variable theories in quantum mechanics necessarily admit contextuality. This theorem is formally stated in terms of the partial Boolean algebra structure of projectors on a Hilbert…
3D Convolution Neural Networks (CNNs) have been widely applied to 3D scene understanding, such as video analysis and volumetric image recognition. However, 3D networks can easily lead to over-parameterization which incurs expensive…
Within the framework of quantum contextuality, we discuss the ideas of extracontextuality and extravalence, that allow one to relate Kochen-Specker's and Gleason's theorems. We emphasize that whereas Kochen-Specker's is essentially a no-go…
If noncontextuality is defined as the robustness of a system's response to a measurement against other simultaneous measurements, then the Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality. Namely, for the…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
We present a novel corpus of 445 human- and computer-generated documents, comprising about 27,000 clauses, annotated for semantic clause types and coherence relations that allow for nuanced comparison of artificial and natural discourse…
A number of new proofs of the Kochen-Specker theorem are given based on the observables of the three-qubit Pauli group. Each proof is presented in the form of a diagram from which it is obvious by inspection. Each of our observable-based…