Related papers: Structure of Uniformly Continuous Quantum Markov S…
Invariance properties of linear functionals and linear maps on algebras of functions on quantum homogeneous spaces are studied, in particular for the special case of expected coideal *-subalgebras. Several one-to-one correspondences between…
The von Neumann type subsystems of $q$-deformed coherent states are considered. The completeness of such subsystems is proved.
We characterize a class of superclassical non-Markovian open quantum system dynamics that are defined by their lack of measurement invasiveness when the corresponding observable commutates with the pre-measurement state. This diagonal…
Non-Markovian effects in quantum evolution appear when the system is strongly coupled to the environment and interacts with it for long periods of time. To include memory effects in the master equations, one usually incorporates time-local…
Quantum coherence, the physical property underlying fundamental phenomena such as multi-particle interference and entanglement, has emerged as a valuable resource upon which exotic modern technologies are founded. In general, the most…
The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction…
Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantum computing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and…
Continuous quantum measurement is the backbone of various methods in quantum control, quantum metrology, and quantum information. Here, we present a generalized formulation of dispersive measurement of a complex quantum systems. We describe…
We study the decoherence properties of a certain class of Markovian quantum open systems from both the Decohering Histories and Environment Induced Superselection paradigms. The class studied includes many familiar quantum optical cases.…
Modern quantum information theory provides new tools for investigating the decoherence-induced "classicality" of open quantum systems. Recent observation that almost all quantum states bear non-classical correlations [A. Ferraro {\it et…
A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully flat quantum homogeneous…
The thesis is contributed to the study of the decoherence dynamics of dissipative qubit systems. We reveal the profound impact of the formation of a bound state between the qubit and its local environment on the decoherence dynamics of…
We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…
The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general…
Open quantum systems exhibit a rich phenomenology, in comparison to closed quantum systems that evolve unitarily according to the Schr\"odinger equation. The dynamics of an open quantum system are typically classified into Markovian and…
Quantum devices are subject to natural decay. We propose to study these decay processes as the Markovian evolution of quantum channels, which leads us to dynamical semigroups of superchannels. A superchannel is a linear map that maps…
We introduce a class of so called Markovian marginals, which gives a natural framework for constructing solutions to the quantum marginal problem. We consider a set of marginals that possess a certain internal quantum Markov chain…
This paper provides a general theory for characterizing and constructing a decoherence-free (DF) subsystem for an infinite dimensional linear open quantum system. The main idea is that, based on the Heisenberg picture of the dynamics rather…
The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on…
Understanding the far-from-equilibrium dynamics of dissipative quantum systems, where dissipation and decoherence coexist with unitary dynamics, is an enormous challenge with immense rewards. Often, the only realistic approach is to forgo a…