Related papers: Included-row exchange principle for quantum minors
We show that given a finitely generated standard-graded algebra of dimension $d$ over an infinite field, its graded Noether normalizations obey a certain kind of `generic exchange', allowing one to pass between any two of them in at most…
This paper offers a proof of the Coase theorem by formalizing the notion of ideal exchanges.
In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for…
Quantum information and quantum foundations are becoming popular topics for advanced undergraduate courses. Many of the fundamental concepts and applications in these two fields, such as delayed choice experiments and quantum encryption,…
To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…
In this work we present a general mathematical framework to deal with Quantum Networks, i.e. networks resulting from the interconnection of elementary quantum circuits. The cornerstone of our approach is a generalization of the Choi…
We give a combinatorial proof of a theorem of Gromov, which extends the scope of small cancellation theory to group presentations arising from labelled graphs.
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem of congruence commutators for loops relates generators of the…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
We present two new proofs of the the important q-commuting property holding among certain pairs of quantum minors of an n x n q-generic matrix. The first uses elementary quasideterminantal arithmetic; the second involves paths in an…
We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…
Recent advances in classical machine learning have shown that creating models with inductive biases encoding the symmetries of a problem can greatly improve performance. Importation of these ideas, combined with an existing rich body of…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
In this article we construct a large family of $R$-matrices for various extensions of small quantum groups by grouplike elements. The extensions are in correspondence to lattices between root and weight lattice and admit $R$-matrices in…
We produce neccessary and sufficient conditions for pairs of quantum minors in the quantized coordinate algebra $\Bbb{C}_q[Mat_{k \times m}]$ to quasi-commute. In addition we study the combinatorics of maximal (by inclusion) families of…
Results obtained by us are overviewed from a general set up. The universal $R$-matrix is exploited to obtain various important relations and structures involved in quantum group algebra, which are used subsequently for generating different…
A key aspect of a recent proposal for a {\em generalized loop representation} of quantum Yang-Mills theory and gravity is considered. Such a representation of the quantum theory has been expected to arise via consideration of a particular…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…