Related papers: Steering a quantum system over a Schroedinger brid…
Elaborating on M. Pavon, J.Math. Phys. 40 (1999), 5565-5577, we develop a simplified version of a variational principle within Nelson stochastic mechanics that produces the von Neumann wave packet reduction after a position measurement.…
Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets,…
We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control…
We have advocated in a previous paper (Godart M. arXiv: 1206.2917v2[quant-ph] ) a version of the stochastic theory of quantum mechanics. It is indirectly based on a method proposed by Nelson to associate a Markov process with any solution…
Steering is a physical phenomenon which is not restricted to quantum theory, it is also present in more general, no-signalling theories. Here, we study steering from the point of view of no-signalling theories. First, we show that quantum…
Quantum steering has been exploited as an important resource in modern quantum information processing. Owing to its directional nature, some quantum states that are asymmetric under the exchange of parties have been found to manifest…
The subject of this work has its roots in the so called Schroedginer Bridge Problem (SBP) which asks for the most likely distribution of Brownian particles in their passage between observed empirical marginal distributions at two distinct…
The effect of quantum steering describes a possible action at a distance via local measurements. In the last few years, several criteria have been proposed to detect this type of correlation in quantum systems. However, there are few…
The classical Schrodinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and…
Quantum correlations between two parties are essential for the argument of Einstein, Podolsky, and Rosen in favour of the incompleteness of quantum mechanics. Schr\"odinger noted that an essential point is the fact that one party can…
A general time-dependent quantum system can be driven fast from its initial ground state to its final ground state without generating transitions by adding a steering term to the Hamiltonian. We show how this technique can be modified to…
We take a new look at the relation between the optimal transport problem and the Schr\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing…
We apply the method of transitionless quantum driving for time-dependent quantum systems to spin systems. For a given Hamiltonian, the driving Hamiltonian is constructed so that the adiabatic states of the original system obey the…
The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…
This work addresses the optimal covariance control problem for stochastic discrete-time linear time-varying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian…
Quantum counterparts of Schrodinger's classical bridge problem have been around for the better part of half a century. During that time, several quantum approaches to this multifaceted classical problem have been introduced. In the present…
Quantifying entanglement is an important task by which the resourcefulness of a quantum state can be measured. Here, we develop a quantum algorithm that tests for and quantifies the separability of a general bipartite state by using the…
It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous…
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…
Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition…