Related papers: Universal Properties in Quantum Theory
From a theory of an abstract quantum information the theory of general relativity can be deduced by means of few and physically good founded reasons. "Abstract" quantum information means that primarily no special meaning is connected with…
In this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to…
We describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these…
Quantum process tomography, the standard procedure to characterize any quantum channel in nature, is affected by a circular argument: in order to characterize the channel, the tomographic preparation and measurement need in turn to be…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
We address the problem of existence of completely positive trace preserving (CPTP) maps between two sets of density matrices. We refine the result of Alberti and Uhlmann and derive a necessary and sufficient condition for the existence of a…
We consider the classical concept of time of permanence and observe that its quantum equivalent is described by a bona fide self-adjoint operator. Its interpretation, by means of the spectral theorem, reveals that we have to abandon not…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
Using Grothendieck approach to the tensor product of locally convex spaces we review a characterization of positive maps as well as Belavkin-Ohya characterization of PPT states. Moreover, within this scheme, \textit{ a generalization of the…
Many insights into the quantum world can be found by studying it from amongst more general operational theories of physics. In this thesis, we develop an approach to the study of such theories purely in terms of the behaviour of their…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
We show that either of the two reasonable choices for the category of compact quantum groups is nice enough to allow for a plethora of universal constructions, all obtained "by abstract nonsense" via the adjoint functor theorem. This…
In quantum mechanics, often it is important for the representation of quantum system to study the structure-preserving bijective maps of the quantum system. Such maps are also called isomorphisms or automorphisms. In this note, using the…
For certain roots of unity, we consider the categories of weight modules over three quantum groups: small, un-restricted and unrolled. The first main theorem of this paper is to show that there is a modified trace on the projective modules…
In this paper is presented an abstract theory of quantum processors and controllers, special kind of quantum computational network defined on a composite quantum system with two parts: the controlling and controlled subsystems. Such…
We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure.
A quantum holonomy reflects the curvature of some underlying structure of quantum mechanical systems, such as that associated with quantum states. Here, we extend the notion of holonomy to families of quantum channels, i.e., trace…
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at…
We consider applications of transfer operators (also known as Ruelle operators) to completely positive maps (CPT) in quantum information theory. It is described a correspondence between fixed points of CPT maps and certain Markov-invariant…