Related papers: A general framework for complete positivity
We show that the entanglement evolution of an open quantum system is the same for the vast majority of initial pure states, in the limit of large Hilbert space dimensions.
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…
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently…
The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we…
Quantum measurement is a physical process. What physical resources and constraints does quantum mechanics require for measurement to produce the classical world we observe? Treating measurement as a fully unitary quantum process, our goal…
We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
We investigated the possibility that a single measurement run with a definite outcome is a joint unitary evolution of all the participating systems, and measurement runs with different definite outcomes correspond to different unitary maps.…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum…
The standard theoretical descriptions of the dynamics of open quantum systems rely on the assumption that the correlations with the environment can be neglected at some reference (initial) time. While being reasonable in specific instances,…
The article establishes a framework for dynamic generation of informationally complete POVMs in quantum state tomography. Assuming that the evolution of a quantum system is given by a dynamical map in the Kraus representation, one can…
State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under…
Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
This paper presents a constructive proof of complete kinematic state controllability of finite-dimensional open quantum systems whose dynamics are represented by Kraus maps. For any pair of states (pure or mixed) on the Hilbert space of the…
Starting from the observation that reversible processes cannot increase the purity of any input state, we study deterministic physical processes, which map a set of states to a set of pure states. Such a process must map any state to the…