Related papers: The bicrossed product construction for locally com…

We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a…

In this paper we use the recent developments in the representation theory of locally compact quantum groups, to assign, to each locally compact quantum group $\mathbb{G}$, a locally compact group $\tilde \mathbb{G}$ which is the quantum…

In this paper, we carry out the ``quantum double construction'' of the specific quantum groups we constructed earlier, namely, the ``quantum Heisenberg group algebra'' (A,\Delta) and its dual, the ``quantum Heisenberg group''…

We study actions of locally compact groups on von Neumann factors and the associated crossed-product von Neumann algebras. In the setting of totally disconnected groups we provide sufficient conditions on an action $G\curvearrowright Q$…

We prove that a family of at least two non-trivial, almost-connected locally compact groups cannot have a coproduct in the category of locally compact groups if at least one of the groups is connected; this confirms the intuition that…

We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and…

Starting from any proper action of any locally compact quantum group on any discrete quantum space, we show that its equivariant representation theory yields a concrete unitary 2-category of finite type Hilbert bimodules over the discrete…

An algorithm is proposed for constructing quasi-random "peaked" quantum circuits, i.e., circuits whose final qubit state exhibits a high probability concentration on a specific computational basis state. These circuits consist of random…

In this paper, we give some properties of the fixed point algebra and the crossed product of a unital separable simple infinite dimensional C*-algebra by an action of a second-countable compact group with the tracial Rokhlin property with…

We introduce a notion of partition wreath product of a finite group by a partition quantum group, a construction motivated on the one hand by classical wreath products and on the other hand by the free wreath product of J. Bichon. We…

We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples…

Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct…

We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups. Several new quantum groups constructed by Banica, Curran and Speicher since the…

We show that every topological k-graph constructed from a locally compact Hausdorff space {\Omega} and a family of pairwise commuting local homeomorphisms on {\Omega} satisfying a uniform boundedness condition on the cardinalities of…

We consider the hidden subgroup problem on the semi-direct product of cyclic groups $\Z_{N}\rtimes\Z_{p}$ with some restriction on $N$ and $p$. By using the homomorphic properties, we present a class of semi-direct product groups in which…

The theory of measured quantum groupoids, as defined by Lesieur and myself, was made to generalize the theory of quantum groups made by Kustarmans and Vaes, but was only defined in a von Neumann algebra setting; Th. Timmermann constructed…

In this paper, we present a characterization of compact quantum metric spaces in terms of finite dimensional approximations. This characterization naturally leads to the introduction of a matrix analogue of a compact quantum metric space.…

We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…

Let $A$ be a Hopf algebra in a braided category $\cal C$. Crossed modules over $A$ are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category $\DY{\cal C}^A_A$ of…

The paper presents a construction of the crossed product of a C*-algebra by a semigroup of endomorphisms generated by partial isometries.