53 citations · 256 across the 21 of their papers we have counts for
21 papers
The Floquet-Magnus expansion of unbounded operators
Daniel Burgarth, Robin Hillier, Davide Lonigro +1
The Floquet-Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamilto…
From vertex operator superalgebras to graded-local conformal nets and back
Sebastiano Carpi, Tiziano Gaudio, Robin Hillier
We generalize the Carpi-Kawahigashi-Longo-Weiner correspondence between vertex operator algebras and conformal nets to the case of vertex operator superalgebras and graded-local co…
Taming the Rotating Wave Approximation
Daniel Burgarth, Paolo Facchi, Robin Hillier +1
The interaction between light and matter is one of the oldest research areas of quantum mechanics, and a field that just keeps on delivering new insights and applications. With the…
Haploid algebras in -tensor categories and the Schellekens list
Sebastiano Carpi, Tiziano Gaudio, Luca Giorgetti +1
We prove that a haploid associative algebra in a -tensor category is equivalent to a Q-system (a special -Frobenius algebra) in if and only if…
Stability and convergence of dynamical decoupling with finite amplitude control
Daniel Burgarth, Paolo Facchi, Robin Hillier
Dynamical decoupling is a key method to mitigate errors in a quantum mechanical system, and we studied it in a series of papers dealing in particular with the problems arising from…
Control of quantum noise: on the role of dilations
Daniel Burgarth, Paolo Facchi, Robin Hillier
We show that every finite-dimensional quantum system with Markovian (i.e., GKLS-generated) time evolution has an autonomous unitary dilation which can be dynamically decoupled. Sin…
Non-Markovian noise that cannot be dynamically decoupled by periodic spin echo pulses
Daniel Burgarth, Paolo Facchi, Martin Fraas +1
Dynamical decoupling is the leading technique to remove unwanted interactions in a vast range of quantum systems through fast rotations. But what determines the time-scale of such…
Roots of Completely Positive Maps
B. V. Rajarama Bhat, Robin Hillier, Nirupama Mallick +1
We introduce the concept of completely positive roots of completely positive maps on operator algebras. We do this in different forms: as asymptotic roots, proper discrete roots an…
Classification of unitary vertex subalgebras and conformal subnets for rank-one lattice chiral CFT models
Sebastiano Carpi, Tiziano Gaudio, Robin Hillier
We provide a complete classification of unitary subalgebras of even rank-one lattice vertex operator algebras. As a consequence of the correspondence between vertex operator algebr…
Dynamical Decoupling of Unbounded Hamiltonians
Christian Arenz, Daniel Burgarth, Paolo Facchi +1
We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the…
Dynamical Decoupling and Homogenization of continuous variable systems
Christian Arenz, Robin Hillier, Daniel Burgarth
For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum…
Loop groups and noncommutative geometry
Sebastiano Carpi, Robin Hillier
We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the le…
A continuous-time diffusion limit theorem for dynamical decoupling and intrinsic decoherence
Robin Hillier, Christian Arenz, Daniel Burgarth
We discuss a few mathematical aspects of random dynamical decoupling, a key tool procedure in quantum information theory. In particular, we place it in the context of discrete stoc…
Distinguishing decoherence from alternative quantum theories by dynamical decoupling
Christian Arenz, Robin Hillier, Martin Fraas +1
A longstanding challenge in the foundations of quantum mechanics is the verification of alternative collapse theories despite their mathematical similarity to decoherence. To this…
Local-entire cyclic cocycles for graded quantum field nets
Robin Hillier
In a recent paper we studied general properties of super-KMS functionals on graded quantum dynamical systems coming from graded translation-covariant quantum field nets over R, and…
Superconformal nets and noncommutative geometry
Sebastiano Carpi, Robin Hillier, Roberto Longo
This paper provides a further step in our program of studying superconformal nets over S^1 from the point of view of noncommutative geometry. For any such net A and any family Delt…
N=2 superconformal nets
Sebastiano Carpi, Robin Hillier, Yasuyuki Kawahigashi +2
We provide an Operator Algebraic approach to N=2 chiral Conformal Field Theory and set up the Noncommutative Geometric framework. Compared to the N=1 case, the structure here is mu…
Conformal nets and KK-theory
Sebastiano Carpi, Roberto Conti, Robin Hillier
Given a completely rational conformal net A on the circle, its fusion ring acts faithfully on the K_0-group of a certain universal C*-algebra associated to A, as shown in a previou…
Super-KMS functionals for graded-local conformal nets
Robin Hillier
Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speak…
Representations of Conformal Nets, Universal C*-Algebras and K-Theory
Sebastiano Carpi, Roberto Conti, Robin Hillier +1
We study the representation theory of a conformal net A on the circle from a K-theoretical point of view using its universal C*-algebra C*(A). We prove that if A satisfies the spli…
Spectral triples and the super-Virasoro algebra
Sebastiano Carpi, Robin Hillier, Yasuyuki Kawahigashi +1
We construct infinite dimensional spectral triples associated with representations of the super-Virasoro algebra. In particular the irreducible, unitary positive energy representat…