相关论文: State space dimensionality in short memory hidden …

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

A thermodynamic theory is developed to describe the behavior of the entanglement between the coin and position degrees of freedom of the quantum walk on the line. This theory shows that, in spite of the unitary evolution, a steady state is…

The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…

We aim to give a pedagogic presentation of the open system dynamics of a periodically driven qubit in contact with a temperature bath. We are specifically interested in the thermodynamics of the qubit. It is well known that by combining the…

Several recent studies have demonstrated the utility of the quantum SWITCH as an important resource for enhancing the performance of various information processing tasks. In a quantum SWITCH, the advantages appear significantly due to the…

We present a family of three-qubit quantum states with a basic local hidden variable model. Any von Neumann measurement can be described by a local model for these states. We show that some of these states are genuine three-partite…

In this paper we prove that the asymptotic rate of exponential loss of memory of a finite state hidden Markov model is bounded above by the difference of the first two Lyapunov exponents of a certain product of matrices. We also show that…

The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk…

This paper discusses the functional stability of closed-loop Markov Chains under optimal policies resulting from a discounted optimality criterion, forming Markov Decision Processes (MDPs). We investigate the stability of MDPs in the sense…

Numerous real-world control problems involve dynamics and objectives affected by unobservable hidden parameters, ranging from autonomous driving to robotic manipulation, which cause performance degradation during sim-to-real transfer. To…

We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting…

This paper considers hidden Markov models where the observations are given as the sum of a latent state which lies in a general state space and some independent noise with unknown distribution. It is shown that these fully nonparametric…

To make sense of the world around us, we develop models, constructed to enable us to replicate, describe, and explain the behaviours we see. Focusing on the broad case of sequences of correlated random variables, i.e., classical stochastic…

It is well known that the state operator of an open quantum system can be generically represented as the solution of a time-local equation -- a quantum master equation. Unraveling in quantum trajectories offers a picture of open system…

We introduce the Reduced-Rank Hidden Markov Model (RR-HMM), a generalization of HMMs that can model smooth state evolution as in Linear Dynamical Systems (LDSs) as well as non-log-concave predictive distributions as in…

It has been suggested that Ho\v{r}ava-Witten theory could provide a concrete realization of the Dark Dimension Scenario. In this context, the observable Standard Model sector is naturally localized in the micron-sized large dimension, which…

Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…

Recently, it has been argued that quantum mechanics is a complete theory, and that different quantum states do necessarily correspond to different elements of reality, under the assumptions that quantum mechanics is correct and that…

Modeling the environment of a single qubit as an N dimensional quantum system, we show that the dynamics of the qubit alone, if measured in sufficient detail, can reveal the parameters of the qubit-environment coupling Hamiltonian. We show…

Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions. We use HMM's as denotations of…