Related papers: Complete positivity and contextuality of quantum d…
We consider Markovian open quantum dynamics with weak unitary symmetries. Starting from the quantum master equation for the system alone, it is known that the joint dynamics of the system and its environment can be obtained by dilation,…
We describe $\omega$-limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior and the states contained in it commute with each other.…
The dynamics of quantum systems are generally described by a family of quantum channels (linear, completely positive and trace preserving maps). In this note, we mainly study the range of all possible values of…
Quantum maps are fundamental to quantum information theory and open quantum systems. Covariant or weakly symmetric quantum maps, in particular, play a key role in defining quantum evolutions that respect thermodynamics, establish free…
It is shown that if the decoherence matrix corresponding to a qubit master equation has a block-diagonal real part, then the evolution is determined by a one-dimensional oscillator equation. Further, when the full decoherence matrix is…
The representation of measurements by positive operator valued measures and the description of the most general state transformations by means of completely positive maps are two basic concepts of quantum information theory. These concepts…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
The time evolution of an initially uncorrelated system is governed by a completely positive (CP) map. More generally, the system may contain initial (quantum) correlations with an environment, in which case the system evolves according to a…
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…
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first con- tribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i)…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
We derive an extremal equation for optimal completely-positive map which most closely approximates a given transformation between pure quantum states. Moreover, we also obtain an upper bound on the maximal mean fidelity that can be attained…
Two kinds of maps that describe evolution of states of a subsystem coming from dynamics described by a unitary operator for a larger system, maps defined for fixed mean values and maps defined for fixed correlations, are found to be quite…
Quantum coherence is the most fundamental feature of quantum mechanics. The usual understanding of it depends on the choice of the basis, that is, the coherence of the same quantum state is different within different reference framework. To…
It is shown in the paper that the unitary quantum dynamics in quantum mechanics is the universal quantum driving force to speed up a quantum computation. This assertion supports strongly in theory that the unitary quantum dynamics is the…
The ultimate goal of this paper is to develop a systematic method for deriving quantum master equations that satisfy the requirements of a completely positive and trace-preserving (CPTP) map, further describing thermal relaxation processes.…
Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
Entanglement of states and Complete Positivity of maps are concepts that have achieved physical importance with the recent growth of quantum information science. They are however mathematically relevant whenever tensor products of complex…