Related papers: State space dimensionality in short memory hidden …
We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation…
In this study, we consider three dark energy models in which $\Lambda$ is not constant, but has a dynamic nature that depends on the Hubble parameter $H$ and/or its time derivative $\dot{H}$. We analyze the generalized running vacuum model,…
We introduce a new procedure to neuralize unsupervised Hidden Markov Models in the continuous case. This provides higher flexibility to solve problems with underlying latent variables. This approach is evaluated on both synthetic and real…
We discuss the properties of the dynamics of purely memristive circuits using a recently derived consistent equation for the internal memory variables of the involved memristors. In particular, we show that the number of independent memory…
We construct a minimal dynamical system of mean dimension equal to $1$, which can be embedded in the shift action on the Hilbert cube $[0,1]^\mathbb{Z}$. This clarifies a seemingly plausible impression about embedding possibility in…
Do diffusive non-Markovian stochastic Schr\"odinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation…
Master equations are commonly used to model the dynamics of physical systems, including systems that implement single-valued functions like a computer's update step. However, many such functions cannot be implemented by any master equation,…
Many systems in biology, physics, and engineering are modeled by nonlinear dynamical systems where the states are usually unknown and only a subset of the state variables can be physically measured. Can we understand the full system from…
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…
Quantum circuit dynamics with local projective measurements can realize a rich spectrum of entangled states of quantum matter. Motivated by the physics of the Kitaev quantum spin liquid [1], we study quantum circuit dynamics in…
The statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. However, inferring the physical properties from the observed trajectories is challenging. Inspired by a…
In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…
Suppose we want to benchmark a quantum device held by a remote party, e.g. by testing its ability to carry out challenging quantum measurements outside of a free set of measurements $\mathcal{M}$. A very simple way to do so is to set up a…
I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional…
Quantum mechanics implies that not all physical properties can be simultaneously well defined, such as the momentum and position due to Heisenberg uncertainty principle. Some alternative theories have been explored, notably the…
We consider an energy storage problem involving a wind farm with a forecasted power output, a stochastic load, an energy storage device, and a connection to the larger power grid with stochastic prices. Electricity prices and wind power…
Recurrent quantum models (RQMs) realize sequential quantum processes through repeated application of a unitary operation on a memory system coupled with a series of output registers. However, such models often rely on unnecessarily large…
Non-Markovian processes may arise in physics due to memory effects of environmental degrees of freedom. For quantum non-Markovianity, it is an ongoing debate to clarify whether such memory effects have a verifiable quantum origin, or…
The study of quantum dynamics featuring memory effects has always been a topic of interest within the theory of open quantum system, which is concerned about providing useful conceptual and theoretical tools for the description of the…
A witness of non-Markovianity based on the Hilbert-Schmidt speed (HSS), a special type of quantum statistical speed, has been recently introduced for low-dimensional quantum systems. Such a non-Markovianity witness is particularly useful,…