Related papers: A Geometrical Approach to Quantum Estimation Theor…
Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but…
In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential…
This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic…
This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…
We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and…
Contents: 1. Introduction 2. Bosonic propagators and random paths 3. Random surfaces and strings 4. Matrix models and two-dimensional quantum gravity 5. The mystery of $c > 1$ 6. Euclidean quantum gravity in $d > 2$ 7. Discussion
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Left on its own, a quantum state evolves deterministically under the Schr\"odinger Equation, forming superpositions. Upon measurement, however, a stochastic process governed by the Born rule collapses it to a single outcome. This dual…
We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…
It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have about an individual system [5, 18].These are so called…
Black Holes have always played a central role in investigations of quantum gravity. This includes both conceptual issues such as the role of classical singularities and information loss, and technical ones to probe the consistency of…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally…
The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears…
Approximation methods for calculating individual particle/ field motions in spacetime at the quantum level of accuracy (a key feature of the Bohm Picture of Quantum Mechanics (BP)), are studied. Modern textbook presentations of Quantum…
Quantum state tomography (QST) aims at estimating a quantum state from averaged quantum measurements made on copies of the state. Most quantum algorithms rely on QST at some point and it is a well explored topic in the literature, mostly…
Conformal field theories have been extremely useful in our quest to understand physical phenomena in many different branches of physics, starting from condensed matter all the way up to high energy. Here we discuss applications of…
We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of…
This book gives a geometry-first, hardware-aware route through quantum-information workflows, with one goal: connect states, circuits, and measurement to deterministic classical pipelines that make hybrid quantum systems run. Part 1…