Related papers: Quantum Hyperdeterminants and Hyper-Pfaffians
We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational…
The recently introduced quantum antibracket is further generalized allowing for the defining odd operator Q to be arbitrary. We give exact formulas for higher quantum antibrackets of arbitrary orders and their generalized Jacobi identities.…
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.
The "quantum duality principle" states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie…
We develop a general theory of `quantum' diffeomorphism groups based on the universal comeasuring quantum group $M(A)$ associated to an algebra $A$ and its various quotients. Explicit formulae are introduced for this construction, as well…
We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…
Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the…
A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.
Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…
We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of 'quantum' type in all but a few exceptional cases.
This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…
It is proved that a quantum computer with fixed and permanent interaction of diagonal type between qubits proposed in the work quant-ph/0201132 is universal. Such computer is controlled only by one-qubit quick transformations, and this…
Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension $\geq 3$, tighten existing bounds --…
We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups,…
In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…
We generalize linear superalgebra to higher gradings and commutation factors, given by arbitrary abelian groups and bicharacters. Our central tool is an extension, to monoidal categories of modules, of the Nekludova-Scheunert faithful…
Supersymmetric and parasupersymmetric quantum mechanics are now recognized as two further parts of quantum mechanics containing a lot of new informations enlightening (solvable) physical applications. Both contents are here analysed in…
Starting with some determinants of binomial coefficients which are related to Fibonacci and Lucas polynomials we study similar determinants for some generalizations of these polynomials and their q-analogues.
A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…