Related papers: Divisibility of dynamical maps: Schr\"odinger vs. …
Divisibility of dynamical maps turns out to be a fundamental notion in characterising Markovianity of quantum evolution, although the decision problem for divisibility itself is computationally intractable. In this work, we propose the…
The problem of defining quantum non-Markovianity has proven elusive, with various in-equivalent criteria put forth to address it. The concept of CP-indivisibility and the hierarchy of stronger divisibility criteria going up to…
In the theory of open quantum systems, divisibility of the system dynamical maps is related to memory effects in the dynamics. By decomposing the system Hilbert space as a direct sum of several Hilbert spaces, we study the relationship…
The concept of divisibility of dynamical maps is used to introduce an analogous concept for quantum channels by analyzing the \textit{simulability} of channels by means of dynamical maps. In particular, this is addressed for Lindblad…
We identify two broad types of noninvertibilities in quantum dynamical maps, one necessarily associated with CP indivisibility and one not so. We study the production of (non-)Markovian, invertible maps by the process of mixing…
We study a stochastic Schroedinger equation that generates a family of Gaussian dynamical maps in one dimension permitting a detailed exam of two different definitions of non-Markovianity: one related to the explicit dependence of the…
Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under…
The standard claim that the Schr\"odinger and Heisenberg pictures of quantum mechanics are equivalent rests on the fact that they yield identical empirical predictions. This equivalence therefore assumes the instrumentalist worldview in…
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…
The role of CP-indivisibility and incompatibility as valuable resources for various information-theoretic tasks is widely acknowledged. This study delves into the intricate relationship between CP-divisibility and channel compatibility. Our…
We analyze two recently proposed measures of non-Markovianity: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a toy model to show that these two…
A notion of differentiability is being proposed for maps between Wasserstein spaces of order 2 of smooth, connected and complete Riemannian manifolds. Due to the nature of the tangent space construction on Wasserstein spaces, we only give a…
We analyze the relation between CP-divisibility and the lack of information backflow for an arbitrary -- not necessarily invertible -- dynamical map. It is well known that CP-divisibility always implies lack of information backflow.…
We study different characterizations of P-divisibility in two-level open quantum systems whose dynamics are governed by a time-local master equation with time-dependent relaxation rates. Necessary and sufficient conditions for the…
We outline a new approach to the characterization as well as to the classification of positive maps. This approach is based on the facial structures of the set of states and of the cone of positive maps. In particular, the equivalence…
This article is the second in a series of two presenting the Scale Relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. Here, we show Schroedinger's equation to be a reformulation of Newton's…
Completely positive trace preserving maps are widely used in quantum information theory. These are mostly studied using the master equation perspective. A central part in this theory is to study whether a given system of dynamical maps…
We introduce a concept of Kadison-Schwarz divisible dynamical maps. It turns out that it is a natural generalization of the well known CP-divisibility which characterizes quantum Markovian evolution. It is proved that Kadison-Schwarz…
Non-P-divisibility is the strongest divisibility-based notion of quantum non-Markovianity. The generalized trace distance (GTD) based criterion is known to be an optimal witness of non-P-divisibility of dynamical maps, in the sense that a…
We construct a dynamical map which is not positive divisible and does not present information backflow either (as measured by trace norm quantifiers). It is formulated for a qutrit system undergoing noninvertible dynamics. This provides an…