Related papers: Spin networks of quantum channels
We argue that notions in quantum theory should have universal properties in the sense of category theory. We consider the completely positive trace preserving (CPTP) maps, the basic notion of quantum channel. Physically, quantum channels…
A spin network is a cubic ribbon graph labeled by representations of $\mathrm{SU}(2)$. Spin networks are important in various areas of Mathematics (3-dimensional Quantum Topology), Physics (Angular Momentum, Classical and Quantum Gravity)…
An alternative framework underlying connection between tensor ${\rm sl}_2$-calculus and spin networks is suggested. New sign convention for the inner product in the dual spinor space leads to a simpler and direct set of initial rules for…
Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be…
The objective of this work is twofold. On one hand, it is intended as a short introduction to spin networks and invariants of 3-manifolds. It covers the main areas needed to have a first understanding of the topics involved in the…
The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrodinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many…
It has been recently shown that in quantum systems, the complex time evolution typical of many-bodied coupled networks can be transformed into a simple, relaxation-like dynamics, by relying on periodic dephasings of the off-diagonal density…
The study of quantum channels is the fundamental field and promises wide range of applications, because any physical process can be represented as a quantum channel transforming an initial state into a final state. Inspired by the method…
We generalize the idea of Vassiliev invariants to the spin network context, with the aim of using these invariants as a kinematical arena for a canonical quantization of gravity. This paper presents a detailed construction of these…
Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural…
The past few years have seen a surge in the application of quantum theory methodologies and quantum-like modeling in fields such as cognition, psychology, and decision-making. Despite the success of this approach in explaining various…
We discuss the action of the configuration operators of loop quantum gravity. In particular, we derive the generalised eigenbasis for the Wilson loop operator and show that the transformation between this basis and the spin-network basis is…
We discuss the universal spin dynamics in quasi one-dimensional systems including the real spin in narrow-gap semiconductors like InAs and InSb, the valley pseudospin in staggered single-layer graphene, and the combination of real spin and…
We consider a quantum channel acting on an infinite dimensional von Neumann algebra of operators on a separable Hilbert space. When there exists an invariant normal faithful state, the cyclic properties of such channels are investigated…
In loop quantum gravity we now have a clear picture of the quantum geometry of space, thanks in part to the theory of spin networks. The concept of `spin foam' is intended to serve as a similar picture for the quantum geometry of spacetime.…
We construct a quantum kinematics for asymptotically flat spacetimes based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying Loop Quantum Gravity (LQG) which supports,…
So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups $\text{SU}(2)_k$ and examine their…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
Loop quantum gravity, a non-perturbative and manifestly background free, quantum theory of gravity implies that at the kinematical level the spatial geometry is discrete in a specific sense. The spirit of background independence also…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…