Related papers: Prediction and Characterization of Multiple Extrem…
In the geometry of quantum evolutions, a geodesic path is viewed as a path of minimal statistical length connecting two pure quantum states along which the maximal number of statistically distinguishable states is minimum. In this paper, we…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
We set up a real-time path integral to study the evolution of quantum systems driven in real-time completely by the coupling of the system to the environment. For specifically chosen interactions, this can be interpreted as measurements…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
This work introduces a novel paradigm for solving optimal control problems for hybrid dynamical systems under uncertainties. Robotic systems having contact with the environment can be modeled as hybrid systems. Controller design for hybrid…
We study the issue of simultaneous estimation of several phase shifts induced by commuting operators on a quantum state. We derive the optimal positive operator-valued measure corresponding to the multiple-phase estimation. In particular,…
Using the adiabatic perturbation theory of driven dynamics [Phys. Rev. A 78, 052508 (2008)] we design a hierarchy of quantum state preparation protocols that systematically increase the fidelity at very long driving times. We test these and…
Predicting human behavior is a difficult and crucial task required for motion planning. It is challenging in large part due to the highly uncertain and multi-modal set of possible outcomes in real-world domains such as autonomous driving.…
We address the dynamics of quantum correlations in continuous variable open systems and analyze the evolution of bipartite Gaussian states in independent noisy channels. In particular, upon introducing the notion of dynamical path through a…
We study monitored quantum dynamics of infinite-range interacting bosonic systems in the thermodynamic limit. We show that under semiclassical assumptions, the quantum fluctuations along single monitored trajectories adopt a deterministic…
The length of time that a quantum system can exist in a superposition state is determined by how strongly it interacts with its environment. This interaction entangles the quantum state with the inherent fluctuations of the environment. If…
Fluctuations play an important role in the dynamics of stochastic systems. In particular, for small systems, the most probable thermodynamic quantities differ from their averages because of the fluctuations. Using the Onsager Machlup…
The dynamics of a quantum-many body system subject to measurements is naturally described by an ensemble of quantum trajectories, which can feature measurement-induced phase transitions (MIPTs). This phenomenon cannot be revealed through…
We prove that transport in the phase space of the "most strongly chaotic" dynamical systems has three different stages. Consider a finite Markov partition (coarse graining) $\xi$ of the phase space of such a system. In the first short times…
A dynamical quantum phase transition can occur during time evolution of sudden quenched quantum systems across a phase transition. It corresponds to the nonanalytic behavior at a critical time of the rate function of the quantum state…
We study a quantum walk of a single particle that is subject to stroboscopic projective measurements on a graph with two sites. This two-level system is the minimal model of a measurement induced quantum walk. The mean first detected…
Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the…
Quantum trajectories are Markov chains modeling quantum systems subjected to repeated indirect measurements. Their stationary regime depends on what observables are measured on the probes used to indirectly measure the system. In this…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
A quantum random walk model is established on a one-dimensional periodic lattice that fluctuates between two possible states. This model is defined by Lindblad rate equations that incorporate the transition rates between the two lattice…