Marek Mozrzymas

κ-deformations of D = 4 Weyl and conformal symmetries ∗

Abstract We provide first explicit examples of quantum deformations of D=4 conformal algebra with mass-like deformation parameters, in applications to quantum gravity effects related with Planck mass. It is shown that one of the classical r-matrices defined on the Borel subalgebra of sl(4) with o(4,2) reality conditions describes the light-cone κ-deformation of D=4 Poincare algebra. We embed this deformation into the three-parameter family of generalized κ-deformations, with r-matrices depending additionally on the dilatation generator. Using the extended Jordanian twists framework we describe these deformations in the form of noncocommutative Hopf algebra. We describe also another four-parameter class of generalized κ-deformations, which is obtained by continuous deformation of distinguished κ-deformation of D=4 Weyl algebra, called here the standard κ-deformation of Weyl algebra.

Convergence to equilibrium under a random Hamiltonian.

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

N = \frac{1}{2} deformations of chiral superspaces from new quantum Poincaré and Euclidean superalgebras

A bstractWe present a large class of supersymmetric classical r-matrices, describing the supertwist deformations of Poincaré and Euclidean superalgebras. We consider in detail new family of four supertwists of N = 1 Poincaré superalgebra and provide as well their Euclidean counterpart. The proposed supertwists are better adjusted to the description of deformed D = 4 Euclidean supersymmetries with independent left-chiral and right-chiral supercharges. They lead to new quantum superspaces, obtained by the superextension of twist deformations of spacetime providing Lie-algebraic noncommutativity of space-time coordinates. In the Hopf-algebraic Euclidean SUSY framework the considered supertwist deformations provide an alternative to the

Structure and properties of the algebra of partially transposed permutation operators

N = \frac{1}{2}

Racah coefficients and 6−j symbols for the quantum superalgebra Uq(osp(1‖2))

SUSY Seiberg’s star product deformation scheme.

Using non-positive maps to characterize entanglement witnesses

We consider the structure of algebra of operators, acting in n-fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its regular representation, we derive basic properties of the algebra. In particular, we describe all irreducible representations of the algebra of partially transposed operators and derive expressions for matrix elements of the representations. It appears that there are two kinds of irreducible representations of the algebra. The first one is strictly connected with the representations of the group S(n − 1) induced by irreducible representations of the group S(n − 2). The second kind is structurally connected with irreducible representations of the group S(n − 1).

Local random quantum circuits are approximate polynomial-designs: numerical results

The tensor product of three irreducible representations of the quantum superalgebra Uq(osp(1‖2)) is studied and the super‐q analogs of Racah coefficients and 6−j symbols for the quantum superalgebra Uq(osp(1‖2)) are defined. Racah coefficients and 6−j symbols depend on the superspin l and the parity λ which characterize the irreducible representations of Uq(osp(1‖2)) but the dependence on parities can be factored out so that one can define parity independent 6−j symbols. It is shown that the 6−j symbols for the quantum superalgebra Uq(osp(1‖2)) satisfy symmetry properties and orthogonality relations similar to those of the 6−j symbols for quantum algebra Uq(su(2)).

Basic twist quantization of the exceptional Lie algebra g2

In this paper we present a new method for entanglement witnesses construction. We show that to construct such an object we can deal with maps which are not positive on the whole domain, but only on a certain sub-domain. In our approach crucial role play such maps which are surjective between sets

Group-representation approach to1→Nuniversal quantum cloning machines

\mathcal{P}_{k}^d

Commutant structure ofU ⊗(n−1) ⊗U ∗ transformations

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