Related papers: Private Quantum Subsystems and Quasiorthogonal Ope…
In this work, we present a complete spectral study of a family of non-normal operators arising in Reggeon field theory. This family of operators is an original example who permit us to discover the recent theory of physical requirement of…
For given quantum (non-commutative) spaces $\mathbb{P}$ and $\mathbb{O}$ we study the quantum space of maps $\mathbb{M}_{\mathbb{P},\mathbb{O}}$ from $\mathbb{P}$ to $\mathbb{O}$. In case of finite quantum spaces these objects turn out to…
In the context of finite Abelian groups two problems are presented and solved using quantum computing techniques. The first is the well--known Hidden Subgroup Problem, originally solved by Simon in a landmark work. The second is the Fully…
This paper studies properties of q-Jacobi polynomials and their duals by means of operators of the discrete series representations for the quantum algebra U_q(su_{1,1}). Spectrum and eigenfunctions of these operators are found explicitly.…
In this Letter, we construct a set of order parameters for non-Abelian gauge theories which probe directly the unbroken group and are free of the deficiencies caused by quantum fluctuations and gauge fixing which have plagued all previous…
We consider algebras of quantum differential operators, for appropriate bicharacters on a polynomial algebra in one indeterminate and for the coordinate algebra of quantum $n$-space for $n\geq 3$. In the former case a set of generators for…
Algebras with given (anti-)commutativity structure are widespread in quantum mechanics. This structure is captured by quasi-Clifford algebras (QCA): a QCA generated by $\alpha_1, \dots, \alpha_n$ is is given by the relations $\alpha_i^2 =…
A subclass of dynamical semigroups induced by the interaction of a quantum system with an environment is introduced. Such semigroups lead to the selection of a stable subalgebra of effective observables. The structure of this subalgebra is…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
We address the question of identifying degrees of freedom for quantum systems. Typically, quasi-particle descriptions of correlated matter are based upon the canonical algebras of bosons or fermions. Here we highlight that a special class…
Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can…
The notion of an open quantum subgroup of a locally compact quantum group is introduced and given several equivalent characterizations in terms of group-like projections, inclusions of quantum group C*-algebras and properties of respective…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to…
We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties…
Information on quantum systems can be obtained only when they are open (or opened) in relation to a certain environment. As a matter of fact, realistic open quantum systems appear in very different shape. We sketch the theoretical…
We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence are imposed on certain components of the subgrading. This allows us to obtain some useful information about the…
A non-associative quantum mechanics is proposed in which the product of three and more operators can be non-associative one. The multiplication rules of the octonions define the multiplication rules of the corresponding operators with…
A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multi-body observables. One strategy to reduce circuit depth in such algorithms involves…