相关论文: Two-sorted algebraic decompositions of Brookes's s…

We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…

Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…

In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses,…

We introduce hybrid algebras as algebraic semantics for hybrid languages with nominals and, possibly, the satisfaction operator. We establish a duality between hybrid algebras and the descriptive two-sorted general frames of Ten Cate. We…

An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of…

We introduce a method to distribute memory effects among different subspaces of an open two-qubit system's state space. Within the linear optical framework, our system of interest is the polarization of two photons, while the environment…

Split preorders are preordering relations on a domain whose composition is defined in a particular way by splitting the domain into two disjoint subsets. These relations and the associated composition arise in categorial proof theory in…

The purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, following the classical example of divided power algebras. We…

Algebraic model counting unifies many inference tasks on logic formulas by exploiting semirings. Rather than focusing on inference, we consider learning, especially in statistical-relational and neurosymbolic AI, which combine logical,…

A two-parameter quantum deformation of the affine Lie super algebra $osp(2|2)^{(2)}$ is introduced and studied in some detail. This algebra is the first example associated with nonsimply-laced and twisted root systems of a quantum current…

We prove rich algebraic structures of the solution space for 2-layer neural networks with quadratic activation and $L_2$ loss, trained on reasoning tasks in Abelian group (e.g., modular addition). Such a rich structure enables…

The canonical Schmidt decomposition of quantum states is discussed and its implementation to the Quantum Computation Simulator is outlined. In particular, the semiorder relation in the space of quantum states induced by the lexicographic…

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…

Schroedinger's disentanglement [E. Schroedinger, Proc. Cambridge Phil. Soc. 31, 555 (1935)], i. e., remote state decomposition, as a physical way to study entanglement, is carried one step further with respect to previous work in…

In this paper, we propose a framework to extract the algebra of the transformations of worlds from the perspective of an agent. As a starting point, we use our framework to reproduce the symmetry-based representations from the…

We propose in this thesis a new deformation process of Kac-Moody algebras and their representations. The direction of deformation is given by a collection of numbers, called a colouring. The natural numbers lead for example to the classical…

This is a sequel to our paper "Permute, Graph, Map, Derange", involving decomposable combinatorial labeled structures in the exp-log class of type a=1/2, 1, 3/2, 2. As before, our approach is to establish how well existing theory matches…

We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…

The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition,…

Effect algebras and pseudoeffect algebras were introduced by Foulis, Bennett, Dvurecenskij and Vetterlein as so-called quantum structures which serve as an algebraic axiomatization of the logic of quantum mechanics. A natural question…