Related papers: Geometry and Dynamics of Quantum State Diffusion
The postulates of von Neumann and L\"uders concerning measurements in quantum mechanics are discussed and criticized in the context of a simple model proposed by Gisin. The main purpose of our paper is to analyze some mathematical aspects…
We prove that the quantum measurement process contains the same warping mechanism that occurs in categorical perception, a phenomenon ubiquitous in human perception. This warping causes stimuli belonging to the same category to be perceived…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to…
In this letter, we describe a general mechanism for emergence of a rainbow metric from a quantum cosmological model. This idea is based on QFT on a quantum space-time. Under general assumptions, we discover that the quantum space-time on…
Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a…
Counting statistics of charge transfers in a point contact interacting with an arbitrary quantum system is studied. The theory for the charge specific density matrix is developed, allowing the evaluation of the probability of the outcome of…
We propose a generalization of quantum mechanical equations in the hydrodynamic form by introducing, into the Lagrangian density, terms taking into account the diffusion velocity at zero and finite temperatures and the diffusion pressure…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
It is shown that the homogeneous and isotropic Universe is spatially flat in the limit which takes into account the moments of infinitely large orders of probabilistic distribution of a scale factor with respect to its mean value in the…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
In this thesis we focus on Gaussian quantum metrology in the phase-space formalism and its applications in quantum sensing and the estimation of space-time parameters. We derive new formulae for the optimal estimation of multiple parameters…
Recent advances in diffusion models have demonstrated their remarkable ability to capture complex image distributions, but the geometric properties of the learned data manifold remain poorly understood. We address this gap by introducing a…
Is the dynamical evolution of physical systems objectively a manifestation of information processing by the universe? We find that an affirmative answer has important consequences for the measurement problem. In particular, we calculate the…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
The development of last years in quantum geometrodynamics highlights new problems which were not obvious in its first formulation proposed by Wheeler and DeWitt. At the first stage the main task was to apply known quantization schemes to…
Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of…
In this paper, we calculate in a transparent way the spectral dimension of a quantum spacetime, considering a diffusion process propagating on a fluctuating manifold. To describe the erratic path of the diffusion, we implement a minimal…
Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase space is…
The space of quantum states can be endowed with a metric structure using the second order derivatives of the relative entropy, giving rise to the so-called Kubo-Mori-Bogoliubov inner product. We explore its geometric properties on the…