Related papers: Completely positive projections and biproducts
We develop a framework for Matrix Product Quantum Channels (MPQCs), a one-dimensional tensor-network description of completely positive, trace-preserving maps. We focus on translation-invariant channels, generated by a single repeated…
We generalize categories of spatial partitions in the sense of C\'ebron-Weber by introducing new base partitions. This allows us to construct additional examples of free orthogonal quantum groups but yields the same class of spatial…
Taking a groupoid C*-algebra approach to the study of the quantum complex projective spaces $\mathbb{P}^{n}\left( \mathcal{T}\right) $ constructed from the multipullback quantum spheres introduced by Hajac and collaborators, we analyze the…
State space structure of tripartite quantum systems is analyzed. In particular, it has been shown that the set of states separable across all the three bipartitions [say $\mathcal{B}^{int}(ABC)$] is a strict subset of the set of states…
Motivated by the classical theory of spin structures, we develop a theory for lifting free C$^*$-dynamical systems, a.k.a. noncommutative principal bundles, along central extensions. This theory extends the bundle-theoretic notion of spin…
By working with several specific Poisson-Lie groups arising from Heisenberg Lie bialgebras and by carrying out their quantizations, a case is made for a useful but simple method of constructing locally compact quantum groups. The strategy…
Here we introduce the concept of classical input - quantum output (C-Q) non-signalling boxes, a generalisation of the classical input - classical output (C-C) non-signalling boxes. We argue that studying such objects leads to a better…
We reformulate Pearl's three rules of do-calculus in the language of completely positive (CP) trace-preserving maps, thereby extending them to quantum systems with entanglement. We prove that Rule~2 fails whenever the underlying process…
We associate a pro-C*-algebra to a pro-C*-correspondence and show that this construction generalizes the construction of crossed products by Hilbert pro-C*-bimodules and the construction of pro-C*-crossed products by strong bounded…
The purpose of this paper is to introduce a consistent notion of universal and reduced crossed products by actions and coactions of groups on operator systems and operator spaces. In particular we shall put emphasis to reveal the full power…
We introduce and study the framework of compact metric structures and their associated notions of isomorphisms such as homeomorphic and bi-Lipschitz isomorphism. This is subsequently applied to model various classification problems in…
We consider two apparently separated problems: in the first part of the paper we study the concept of a scalable (approximate) programmable quantum gate (SPQG). These are special (approximate) programmable quantum gates, with nice…
We demonstrate exciting similarities between classical and quantum many body systems whose microscopic dynamics are composed of non-reciprocal three-site facilitated exclusion processes. We show that the quantum analogue of the classical…
The coexistence of quantum and classical signals over the same optical fiber with minimal degradation of the transmitted quantum information is critical for operating large-scale quantum networks over the existing communications…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the…
The cocycle bicrossed product construction allows certain freedom in producing examples of locally compact quantum groups. We give an overview of some recent examples of this kind having remarkable properties.
We show how the C*-algebras of quantum complex projective spaces (standard or nonstandard) are related to groupoids.
We generalize the universal effective quantum number introduced earlier for centrally symmetric problems. The proposed number determines the semiclassical quantization condition for axially symmetric potentials.
Coecke and Heunen described completely positive maps in dagger monoidal categories and the {\sf CP}-infinity construction on these categories in order to construct a category of arbitrary dimensional quantum processes. This article…