Related papers: Quantized recurrence time in iterated open quantum…
The mean evolution of an open quantum system in continuous time is described by a time continuous semigroup of quantum channels (completely positive and trace-preserving linear maps). Baumgartner and Narnhofer presented a general…
We make use of matrix representations of completely positive maps in order to study open quantum dynamics on graphs, with emphasis on quantum walks and the associated trajectories obtained via a monitoring of the position. We discuss the…
We consider the quantum first detection problem for a particle evolving on a graph under repeated projective measurements with fixed rate $1/\tau$. A general formula for the mean first detected transition time is obtained for a quantum walk…
Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time must involve repeated measurements as…
The dynamics of an open quantum system can be described by a quantum operation, a linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to…
Quantum statistics is defined by Hilbert space products between the eigenstates associated with state preparation and measurement. The same Hilbert space products also describe the dynamics generated by a Hamiltonian when one of the states…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain…
We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability…
Measurements on a quantum particle unavoidably affect its state, since the otherwise unitary evolution of the system is interrupted by a non-unitary projection operation. In order to probe measurement-induced effects in the state dynamics…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
Recurrence in the classical random walk is well known and described by the P\'olya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to return to its origin. Under…
We study the time it takes for all states of a finite quantum system to return simultaneously to their original configuration. In particular, we define the recurrence time for a quantum system to be the time at which all time-evolved states…
Unitary dynamics of a quantum system initialized in a selected basis state yields, generically, a state that is a superposition of all the basis states. This process, associated with the quantum information scrambling and intimately tied to…
We consider open quantum walks on a graph, and consider the random variables defined as the passage time and number of visits to a given point of the graph. We study in particular the probability that the passage time is finite, the…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
We put forward a novel approach to study the evolution of an arbitrary open quantum system under a resetting process. Using the framework of renewal equations, we find a universal behavior for the mean first return time that goes beyond…
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…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
How long does it take a quantum particle to return to its origin? As shown previously under repeated projective measurements aimed to detect the return, the closed cycle yields a geometrical phase which shows that the average first detected…
Closed quantum systems follow a unitary time evolution that can be simulated on quantum computers. By incorporating non-unitary effects via, e.g., measurements on ancilla qubits, these algorithms can be extended to open-system dynamics,…