Related papers: Nuclearity properties and $C^*$-envelopes of opera…
We prove that an operator system $\mathcal S$ is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps $\phi_\lambda : \cl S \to M_{n_\lambda}$ and $\psi_\lambda : M_{n_\lambda} \to…
A new model for calculating the structure of bound states of interacting particles is considered. The model takes into account the noncommutativity of the space and impulse operators plus the correlation equations for the indeterminacy of…
We present a brief introduction to the theory of operator limits of random matrices to non-experts. Several open problems and conjectures are given. Connections to statistics, integrable systems, orthogonal polynomials, and more, are…
Relations among von Neumann entropies of different parts of an $N$-partite quantum system have direct impact on our understanding of diverse situations ranging from spin systems to quantum coding theory and black holes. Best formulated in…
Notions of invariance pressure for control systems are introduced based on weights for the control values. The equivalence is shown between inner invariance pressure based on spanning sets of controls and on invariant open covers,…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
We study the entanglement properties of the output state of a universal cloning machine. We analyse in particular bipartite and tripartite entanglement of the clones, and discuss the ``classical limit'' of infinitely many output copies.
We use results on inclusions of free products and extensions of completely positive maps to determine the maximal $C^*$-envelope for upper triangular $3 \times 3$ matrices. We consider these same results in the context of larger upper…
Two different aspects of the description of three- and four-nucleon systems are addressed. The use of bound state like wave functions to describe scattering states in $N-d$ collisions at low energies and the effects of some of the widely…
We use Arveson's notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets which admit minimal presentations. A fully compressed separable operator system necessarily generates…
We presents a unified and concise exposition of key topics in the mathematical theory of open quantum systems, developed within the framework of operator algebras. The manuscript consolidates and extends a series of invited articles…
Following arXiv:2210.12963 [hep-th], we investigate aspects of the time evolution operator regarded as a density operator and associated entanglement-like structures in various quantum systems. These involve timelike separations and…
The purpose of this paper is two-fold: firstly, we give a characterization on the level of non-unital operator systems for when the zero map is a boundary representation. As a consequence, we show that a non-unital operator system arising…
We characterize when a C*-cover admits a C*-dynamical extension of dynamics on an operator algebra in terms of the boundary ideal structure for the operator algebra in its maximal representation and show that the C*-covers that admit such…
We point out three apparent inconsistencies in the treatment of oscillation coherence from reactor neutrino and source neutrino experiments in recent paper "Damping of neutrino oscillations, decoherence and the lengths of neutrino wave…
Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems…
We transcribe a portion of the theory of extensions of C*-algebras to general operator algebras. We also include several new general facts about approximately unital ideals in operator algebras and the C*-algebras which they generate.
This paper studies direct limits of full upper triangular matrix algebras with embeddings which are not *-extendible. A representation of the limit algebra is found so that the generated C*-algebra is the C*-envelope. Some examples are…
This survey article is concerned with the modeling of the kinematical structure of quantum systems in an algebraic framework which eliminates certain conceptual and computational difficulties of the conventional approaches. Relying on the…
We study the mathematical structure of superoperators describing quantum measurements, including the \emph{entangling measurement}--the generalization of the standard quantum measurement that results in entanglement between the measurable…