相关论文: Clifford's theorem for coherent systems

We provide a careful analysis of the structure theorem for the $n$-qudit projective Clifford group and various encoding schemes for its elements. In particular, we derive formulas for evaluation, composition, and inversion. Our results…

This is the second combinatorial proof of the compactness theorem for singular from 1977. In fact it gives a somewhat stronger theorem.

In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the Clifford-Fourier transform on $\mathbb{R}^m$.

In this paper, a fractional version of the Clifford-Fourier transform is introduced, depending on two numerical parameters. A series expansion for the kernel of the resulting integral transform is derived. In the case of even dimension,…

Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…

In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.

We show that the binary representation of the integers has a role to play in many aspects of Clifford algebras.

We ''save'' Bell's Theorem by showing a flaw in Christian's argument.

The dimension of spaces of global sections for line bundles on semistable curves parametrized by the compactified Picard scheme is studied. The theorem of Riemann is shown to hold. The theorem of Clifford is shown to hold in the following…

We propose a scheme for detecting and correcting faults in any Clifford circuit. The scheme is based on the observation that the set of all possible outcome bit-strings of a Clifford circuit is a linear code, which we call the outcome code.…

We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…

This papper aims to present and demonstrate Clifford's version for a generalization of Miquel's theorem with the use of Euclidean geometry arguments only.

Involutions of the Clifford algebra of a quadratic space induced by orthogonal symmetries are investigated.

We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras.…

The structures of the ideals of Clifford algebras which can be both infinite dimensional and degenerate over the real numbers are investigated.

In this paper we investigate how the short-time Fourier transform can be extended in a Clifford setting. We prove some of the main properties of the Clifford short-time Fourier transform such as the orthogonality relation, the…

This paper exhibits a multiplicative and minimal cellular complex which allows explicit and complete (co)homological calculations for the symmetric products of a finite two dimensional CW complex. By considering cohomology, we observe that…

Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…

Clifford codes are a class of quantum error control codes that form a natural generalization of stabilizer codes. These codes were introduced in 1996 by Knill, but only a single Clifford code was known, which is not already a stabilizer…

The algebraic and geometric properties of a novel generalization of Clifford's classical C4 point-circle configuration are analysed. A connection with the integrable quaternionic discrete Schwarzian Kadomtsev-Petviashvili equation is…