相关论文: Nuclearity properties and $C^*$-envelopes of opera…
We study subsystems of open induction which are strongly connected to methods of automated inductive theorem proving. Specifically, we consider systems obtained from restricting induction to atoms, literals, clauses, and dual clauses. We…
The CBH theorem characterises quantum theory within a C*-algebraic framework. Namely, mathematical properties of C*-algebras modelling quantum systems are equivalent to constraints that are information-theoretic in nature: (1)…
We review recent theoretical and experimental advances toward understanding the effects of nuclear spins in confined nanostructures. These systems, which include quantum dots, defect centers, and molecular magnets, are particularly…
We partially characterize nuclearity for the recently introduced class of hypergraph C*-algebras using a tailor-made hypergraph minor relation. The latter is generated by certain operations on hypergraphs which resemble the moves on…
We study the local operator space structure of nuclear $C^*$-algebras. It is shown that a $C^*$-algebra is nuclear if and only if it is an $\OL_{\infty, \la}$ space for some (and actually for every) $\la > 6$. The $\OL_\infty$ constant…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
We introduce methods of characterizing entanglement, in which entanglement measures are enriched by the matrix representations of operators for observables. These observable operator matrix representations can enrich the partial trace over…
We study closedness of the range, adjointability and generalized invertibility of modular operators between Hilbert modules over locally C*-algebras of coefficients. Our investigations and the recent results of M. Frank [Characterizing…
Recently proved weighted Cauchy Scwarz inequality for Hilbert $C^*$-modules leads to many H\"older type inequalities for unitarily invariant norms on Hilbert space operators.
This article has two interpenetrating motifs. One is an exposition of some major ideas and techniques behind the use of block matrices, and especially their positivity properties. This is done by focussing on one major problem:…
Out-of-time-order correlations (OTOCs) characterize the scrambling, or delocalization, of quantum information over all the degrees of freedom of a system and thus have been proposed as a proxy for chaos in quantum systems. Recent…
The capacitance matrix relates potentials and charges on a system of conductors. We review and rigorously generalize its properties, block-diagonal structure and inequalities, deduced from the geometry of system of conductors and analytic…
As a characteristic property of all quantum systems, entanglement participates in many important quantum phenomena. In this proceeding, we employ it in the study of quantum field theories at finite density. We incorporate evaluations of…
Various global characteristics of the coupling between the bound and scattering states are explicitly studied based on realistic Shell Model Embedded in the Continuum. In particular, such characteristics are related to those of the…
We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random…
We investigate theoretically the extension of cavity optomechanics to multiple membrane systems. We describe such a system in terms of the coupling of the collective normal modes of the membrane array to the light fields. We show these…
We explore some basic entanglement features of multiqubit systems that are relevant for the development of algorithms for searching highly entangled states. In particular, we compare the behaviours of multiqubit entanglement measures based…
Notions of topological free entropy and of free capacity are introduced in the $C^*$-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.
We analyse a notion of $C^*$-independence for $\mathbb{Z}_2$-graded $C^*$-algebras. We provide other notions of statistical independence for $\mathbb{Z}_2$-graded von Neumann algebras and prove some relationships between them. We provide a…
Assuming that the e- and (mu- or tau-type) neutrinos start and end "life" as topologically distinct quantum objects, and assuming that topology maintenance is preferred over topology change, both the matrix describing long-distance neutrino…