Related papers: Commuting quantum traces: the case of reflection a…
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…
We consider the junction of multiple one-dimensional systems and study how conserved currents transport at the junction. To characterize the transport process, we introduce reflection/transmission coefficients by applying boundary conformal…
In this paper we introduce a novel notion of probabilistic bisimulation for quantum processes and prove that it is congruent with respect to various process algebra combinators including parallel composition even when both classical and…
A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but subclasses have been studied previously by other authors. The algebras are indexed by double partitions or double flag varieties.…
In this paper we will study $k$-commuting mappings of generalized matrix algebras. The general form of arbitrary $k$-commuting mapping of a generalized matrix algebra is determined. It is shown that under mild assumptions, every…
This paper introduces a new notion of quantum recursion of which the control flow of the computation is quantum rather than classical as in the notions of recursion considered in the previous studies of quantum programming. A typical…
Let $\mathcal{G}$ be a generalized matrix algebra over a commutative ring $\mathcal{R}$, ${\mathfrak q}\colon \mathcal{G}\times\mathcal{G}\longrightarrow \mathcal{G}$ be an $\mathcal{R}$-bilinear mapping and ${\mathfrak T}_{\mathfrak…
We consider the scattering problems of a quantum particle in a system with a single Y-junction and in ring systems with double Y-junctions. We provide new formalism for such quantum mechanical problems. Based on a path integral approach, we…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
We explicitly construct an Archimedean order unit space whose state space is affinely isomorphic to the set of quantum commuting correlations. Our construction only requires fundamental techniques from the theory of order unit spaces and…
We discuss the consistency of the axioms which the definition of quantum Lie algebras is usually based on.
We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate-space formulation. Using a coherent-state basis makes it immediately…
By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the so-called quantum doubles. The role of the function algebra…
For the family of the orthogonal quantum matrix algebras we investigate the structure of their characteristic subalgebras -- special commutative subalgebras, which for the subfamily of the reflection equation algebras appear to be central.…
Trace decreasing quantum operations naturally emerge in experiments involving postselection. However, the experiments usually focus on dynamics of the conditional output states as if the dynamics were trace preserving. Here we show that…
Generalizing our earlier work, we introduce the homogeneous quantum $Z$-algebras for all quantum affine algebras $\alg$ of type one. With the new algebras we unite previously scattered realizations of quantum affine algebras in various…
In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.
This paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations. Specifically, it is proved that if a quantum operation has mutually commuting operation elements that are effects forming…
We express the defining relations of the $q$-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties…