We study locality preserving automorphisms of operator algebras on D-dimensional uniform lattices prime p-dimensional qudits quantum cellular automata (QCAs), specializing in those that are translation invariant (TI), and map every Pauli matrix to a tensor product matrices (Clifford). associate antihermitian forms the unit determinant over Laurent polynomial rings TI Clifford QCA with lattice b...

For smooth projective curves of genus g ≥ 4, the Clifford index is an important invariant which provides a bound for the dimension of the space of sections of a line bundle. This is the first step in distinguishing curves of the same genus. In this paper we generalise this to introduce Clifford indices for semistable vector bundles on curves. We study these invariants, giving some basic propert...

We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to ...

By viewing Clifford algebras as algebras in some suitable symmetric Gr-categories, Albuquerque and Majid were able to give a new derivation of some well known results about Clifford algebras and to generalize them. Along the same line, Bulacu observed that Clifford algebras are weak Hopf algebras in the aforementioned categories and obtained other interesting properties. The aim of this paper i...

We prove that a unitary matrix has an exact representation over the Clifford+T gate set with local ancillas if and only if its entries are in the ring Z[ 1 √ 2 , i]. Moreover, we show that one ancilla always suffices. These facts were conjectured by Kliuchnikov, Maslov, and Mosca. We obtain an algorithm for synthesizing a exact Clifford+T circuit from any such n-qubit operator. We also characte...

It is shown that Bell’s theorem fails for the Clifford algebra valued local realistic variables. This is made evident by exactly reproducing quantum mechanical expectation value for the EPR-Bohm type spin correlations observable by means of a local, deterministic, Clifford algebra valued variable, without necessitating either remote contextuality or backward causation. Since Clifford product of...

During the last fifty years, Clifford analysis has gradually developed to a comprehensive theory offering a direct, elegant, and powerful generalization to higher dimension of the theory of holomorphic functions in the complex plane. In its most simple but still useful setting, flat m-dimensional Euclidean space, Clifford analysis focusses on the so-called monogenic functions, that is, null sol...

Classical information can be completely hidden in the correlations of bipartite quantum systems. However, it is impossible to hide or mask all according no-hiding and no-masking theorems derived recently. Here we show that any set informationally complete states neither hidable nor maskable, thereby strengthening known before. Then, by virtue Hurwitz-Radon matrices (representations Clifford alg...