Related papers: Exploring Grassmann manifolds in topological syste…
We develop a novel approach to Quantum Mechanics that we call Curved Quantum Mechanics. We introduce an infinite-dimensional K\"ahler manifold ${\cal M}$, that we call the state manifold, such that the cotangent space $T_z^*{\cal M}$ is a…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
We propose a generic protocol to experimentally measure the quantum metric tensor, a fundamental geometric property of quantum states. Our method is based on the observation that the excitation rate of a quantum state directly relates to…
The distance conjecture diagnoses viable low-energy effective realisation of consistent theories of quantum gravity by examining their breakdown at infinite distance in their parameter space. At the same time, infinite distance points in…
We investigate notions of complexity of states in continuous quantum-many body systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the…
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…
Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements in particular, through their back-action on the system, may enable…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…
In this paper we use symplectic reduction in an Uhlmann bundle to construct a principal fiber bundle over a general space of unitarily equivalent mixed quantum states. The bundle, which generalizes the Hopf bundle for pure states, gives in…
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively…
We use projection methods to construct (global) quantum states with prescribed reduced (marginal) states, and possibly with some special properties such as having specific eigenvalues, having specific rank and extreme von Neumann or Renyi…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the…
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
Preparation of a non-classically correlated state is the first step of any quantum-enhanced interferometric protocol. An efficient method is the one-axis twisting, which entangles a collection of initially uncorrelated particles by means of…
Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote…