Related papers: Infinite dimensional dynamical maps
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
In this paper, the mathematical framework providing a description of completely positive and trace preserving dynamics of open quantum systems is addressed. Special case of time-dependent Lindbladian governed by periodic Hamiltonian is…
Trace decreasing quantum operations naturally emerge in experiments involving postselection. However, the experiments usually focus on dynamics of the conditional output states as if the dynamics were trace preserving. Here we show that…
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with $n$ copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show…
Markovian master equations (formally known as quantum dynamical semigroups) can be used to describe the evolution of a quantum state $\rho$ when in contact with a memoryless thermal bath. This approach has had much success in describing the…
There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps.…
We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical…
We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the…
We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely…
Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the unitary system…
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…
Characterizing those quantum channels that correspond to Markovian time evolutions is an open problem in quantum information theory, even different notions of quantum Markovianity exist. One such notion is that of infinitesimal Markovian…
It is shown that a large class of quantum dynamical maps on complex matrix algebras governed by time-local Master Equations tend to become entanglement breaking in the course of time. Such situation seems to be generic for quantum evolution…
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…
Comparison of statistical models (experiments) is an important branch of mathematical statistics, which gives deep insights in many aspects of foundation of statistics. So far, there are two quantum versions of the concept: Comparison with…
For many completely positive maps repeated compositions will eventually become entanglement breaking. To quantify this behaviour we develop a technique based on the Schmidt number: If a completely positive map breaks the entanglement with…
Relations between states and maps, which are known for quantum systems in finite-dimensional Hilbert spaces, are formulated rigorously in geometrical terms with no use of coordinate (matrix) interpretation. In a tensor product realization…
The most general description of quantum evolution up to a time $\tau$ is a completely positive tracing preserving map known as a dynamical map $\hat{\Lambda}(\tau)$. Here we consider $\hat{\Lambda}(\tau)$ arising from suddenly coupling a…
The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common…
Using a recently proposed measure for divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a driven spin-$S$ system weakly coupled to a bosonic bath. The complete tomographic knowledge about the…