Related papers: Controllability properties for finite dimensional …
We investigate the problem of what evolutions an open quantum system described by a time-local Master equation can undergo with universal coherent controls. A series of conditions are given which exclude channels from being reachable by any…
Quantum dynamical maps provide suitable mathematical representation of quantum evolutions. It is the very notion of complete positivity which provides a proper mathematical representation of quantum evolution and gives rise to the powerful…
We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a…
We consider a Markov control model in discrete time with countable both state space and action space. Using the value function of a suitable long-run average reward problem, we study various reachability/controllability problems. First, we…
When the environment of an open quantum system is non-Markovian, amplitude and phase flow not only from the system into the environment but also back. Here we show that this feature can be exploited to carry out quantum control tasks that…
The problem of controlling a finite state Markov chain in the presence of an adversary so as to ensure desired performance levels for a vector of objectives is cast in the framework of Blackwell approachability. Relying on an elementary two…
We study non-Markovianity in the exact dynamics of two two-level atoms in a resonant cavity. We find a critical behavior in the form of a Markovian to non-Markovian transition at a finite interatomic distance and a discontinuity in the…
Dual-unitary circuits are a class of locally-interacting quantum many-body systems displaying unitary dynamics also when the roles of space and time are exchanged. These systems have recently emerged as a remarkable framework where certain…
In a topological space, a family of continuous mappings is called universal if its action, in at least one element of the space, is dense. If the mappings are unitary or trace-preserving completely positive, the notion of universality is…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…
In recent years, Arenz et al. proposed the idea of reachable set characterization based on the quantum speed limit (QSL); that is, the reachable set of the target unitary gate in a closed qubit system can be characterized by considering the…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…
The objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. We focus…
Conditions sufficient for a quantum dynamical semigroup (QDS) to be unital are proved for a class of problems in quantum optics with Hamiltonians which are self-adjoint polynomials of any finite order in creation and annihilation operators.…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
Determining the Markovianity and non-Markovianity of a quantum process is a critical problem in the theory of open quantum systems, as their behaviors differ significantly in terms of complexity. It is well recognized that a quantum process…
The quantum master equation (QME), used to describe the Markov process of interaction between atoms and field, has a number of significant drawbacks. It is extremely memory intensive, and also inapplicable to the case of long-term memory in…
A dynamical symmetry is employed to determine the structure of the quantum non-Markovian time-local master equation. Such a structure is composed from two components: scalar kinetic coefficients and the standard quantum Markovian operator…