Related papers: A Quantum Information Geometric Approach to Renorm…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
Recently people started to understand that applications of the mathematical formalism of quantum theory are not reduced to physics. Nowadays, this formalism is widely used outside of quantum physics, in particular, in cognition, psychology,…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
In this paper we: 1) show how the smooth geometry of spaces of normal quantum states over W*-algebras (generalised spaces of density matrices) may be used to substantially enrich the description of quantum dynamics in the algebraic and path…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
The current understanding of renormalization in quantum gravity (QG) is based on the fact that UV divergences of effective actions in the covariant QG models are covariant local expressions. This fundamental statement plays a central role…
Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
We study how information geometry is described by bulk geometry in the gauge/gravity correspondence. We consider a quantum information metric that measures the distance between the ground states of a CFT and a theory obtained by perturbing…
The renormalization group (RG) is a class of theoretical techniques used to explain the collective physics of interacting, many-body systems. It has been suggested that the RG formalism may be useful in finding and interpreting emergent…
We revisit the representation of generalized quantum observables by establishing a geometric picture in terms of their positive operator-valued measures (POVMs). This leads to a clear geometric interpretation of Born's rule by introducing…
We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher…
The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics -- that the information carried by a system is limited -- and, from this principle, to construct the foundations of…
We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the…
We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a…
A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…
Characterizing complex quantum systems is a vital task in quantum information science. Quantum tomography, the standard tool used for this purpose, uses a well-designed measurement record to reconstruct quantum states and processes. It is,…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based…