Related papers: Tomographic Reconstruction of Quantum Metrics
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…
We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in…
Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these `lattice spacing' weights do not have to be independent of the direction of the arrow. We use this…
Chentsov studied Riemannian metrics on the set of probability measures from the point of view of decision theory. He proved that up to a constant factor the Fisher information is the only metric which is monotone under stochastic…
We determine exactly the mass-coupling relation for the simplest multi-scale quantum integrable model, the homogenous sine-Gordon model with two independent mass-scales. We first reformulate its perturbed coset CFT description in terms of…
The quantum geometric tensor (QGT) of a quantum system in a given parameter space captures both the geometry of the state manifold and the topology of the system. While the local QGT elements have been successfully measured in various…
The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical information this tensor…
Perturbation theory of vacuum spherically-symmetric spacetimes (including the cosmological constant) has greatly contributed to the understanding of black holes, relativistic compact stars and even inhomogeneous cosmological models. The…
The reconstruction of the state of a multipartite quantum mechanical system represents a fundamental task in quantum information science. At its most basic, it concerns a state of a bipartite quantum system whose subsystems are subjected to…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
The quantum properties of quantum measurements are indispensable resources in quantum information processing and have drawn extensive research interest. The conventional approach to reveal the quantum properties relies on the reconstruction…
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…
Quantifying quantum entanglement is a pivotal challenge in quantum information science, particularly for high-dimensional systems, due to its computational complexity. This thesis extends the geometric measure of entanglement (GME) to…
The theory of monotone Riemannian metrics on the state space of a quantum system was established by Denes Petz in 1996. In a recent paper he argued that the scalar curvature of a statistically relevant - monotone - metric can be interpreted…
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
We discuss a quantum mechanical indirect measurement method to recover a position dependent Hamilton matrix from time evolution of coherent quantum mechanical states through an object. A mathematical formulation of this inverse problem…
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
Quantum metrology uses quantum states with no classical counterpart to measure a physical quantity with extraordinary sensitivity or precision. Most metrology schemes measure a single parameter of a dynamical process by probing it with a…
Momentum space of a gapped quantum system is a metric space: it admits a notion of distance reflecting properties of its quantum ground state. By using this quantum metric, we investigate geometric properties of momentum space. In…