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The deterministic and time-reversal symmetric dynamics of isolated quantum systems is at odds with irreversible equilibration observed in generic thermodynamic systems. Standard approaches at a reconciliation employ subjective restrictions…
Given a discrete reversible dynamics, we can define a quantum dynamics, which acts on basis states like the classical one, but also allows for superpositions of them. It is a curious fact that in the quantum version, local changes in the…
Most diffusion models assume that the reverse process adheres to a Gaussian distribution. However, this approximation has not been rigorously validated, especially at singularities, where t=0 and t=1. Improperly dealing with such…
We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an…
Diffusion models excel in generating high-quality images. However, current diffusion models struggle to produce reliable images without guidance methods, such as classifier-free guidance (CFG). Are guidance methods truly necessary?…
A perfect quantum state transfer(QST) has been shown in an engineered spin chain with "always-on interaction". Here, we consider a more realistic problem for such a protocol, the quantum decoherence induced by a spatially distributed…
We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than…
This work explores the theoretical and practical foundations of denoising diffusion probabilistic models (DDPMs) and score-based generative models, which leverage stochastic processes and Brownian motion to model complex data distributions.…
Fluctuation theorems based on time-reversal have provided remarkable insight into the non-equilibrium statistics of thermodynamic quantities like heat, work, and entropy production. These types of laws impose constraints on the…
We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this process is non-stationary and its probability…
Denoising Diffusion Probabilistic Models (DDPMs) have achieved impressive performance on various generation tasks. By modeling the reverse process of gradually diffusing the data distribution into a Gaussian distribution, generating a…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
We study the spread of a quantum-mechanical wavepacket in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations…
We address the impossibility of achieving exact time reversal in a system with many degrees of freedom. This is a particular example of the difficult task of "aiming" an initial classical state so as to become a specific final state. We…
We investigate the diffusive behavior of a quantum particle driven by a correlated Gaussian noise. We derive the analytical solution of the joint probability density function and obtain explicit expressions for the mean square momentum and…
We investigate the performance of continuous variable quantum key distribution scheme in a practical setting. More specifically, we take non-ideal error reconciliation procedure into account. The quantum channel connecting the two honest…
Employing a forward diffusion chain to gradually map the data to a noise distribution, diffusion-based generative models learn how to generate the data by inferring a reverse diffusion chain. However, this approach is slow and costly…
By the example of a kicked quartic oscillator we investigate the dynamics of classically chaotic quantum systems with few degrees of freedom affected by persistent external noise. Stability and reversibility of the motion are analyzed in…
The correspondence principle is investigated in the framework of deterministic predictions for individual systems. Exact analytical results are obtained for the quantum and the Liouvillian dynamics of a nonlinear oscillator coupled to a…
A single mechanism, endemic to the standard model of physics, is proposed to explain wavefunction collapse, classical motion, dissipation, equilibration, and the transition from pure quantum mechanics through open system decoherence to the…