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Geometric Phases in Classical and Quantum Mechanics
Preface - Mathematical background - Adiabatic phases in quantum mechanics - Adiabatic phases in classical mechanics - Geometric approach to classical phases - Geometry of quantum evolution -
Spectral Conditions for Positive Maps
We provide partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes the celebrated Choi example of a map
Degree of non-Markovianity of quantum evolution.
We propose a new characterization of non-Markovian quantum evolution based on the concept of non-Markovianity degree. It provides an analog of a Schmidt number in the entanglement theory and reveals
Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective
TLDR
It is shown that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one and harnessing non- Markovianity may improve the efficiency of quantum information processing and communication.
On the Structure of Entanglement Witnesses and New Class of Positive Indecomposable Maps
We construct a new class of positive indecomposable maps in the algebra of d x d complex matrices. Each map is uniquely characterized by a cyclic bistochastic matrix. This class generalizes Choi map
On Partially Entanglement Breaking Channels
Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number for a quantum channel. It enables one to define classes of quantum channels
Operational Characterization of Divisibility of Dynamical Maps.
TLDR
It is proven that the distinguishability of any pair of quantum channels does not increase under divisible maps, in which the full hierarchy of divisibility is isomorphic to the structure of entanglement between system and environment.
Universal Spectra of Random Lindblad Operators.
TLDR
An ensemble of random Lindblad operators, which generate completely positive Markovian evolution in the space of the density matrices, are introduced and the spectral properties of these operators are evaluated by using methods of free probabilities and explained with non-Hermitian random matrix models.
Quantum mechanics of damped systems
We show that the quantization of a simple damped system leads to a self-adjoint Hamiltonian with a family of complex generalized eigenvalues. It turns out that they correspond to the poles of energy
Memory in a Nonlocally Damped Oscillator
We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both
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