Related papers: Requiring linearity leads to complete positivity
In a semiclassically quantized two-dimensional cosmological model, it can be shown that the parameter of the equation of state for the accelerating universe can be positive due to the negative energy density and the negative pressure, which…
Given two sets of quantum states {A_1, ..., A_k} and {B_1, ..., B_k}, represented as sets of density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T, represented as a…
For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case, such as: given a fixed interaction between the system…
We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
Consider a bipartite quantum system S=AB such that each part interacts only with its local environment. Under such circumstances, one expects that the entanglement between parts A and B does not exceed its initial value during the time…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
Dynamical typicality refers to the property that two pure states, which initially exhibit (almost) the same expectation value for some given observable $A$, are very likely to exhibit also very similar expectation values when evolving in…
A quantum mechanical system S is indirectly controlled when the control affects an ancillary system A and the evolution of S is modified through the interaction with A only. A study of indirect controllability gives a description of the set…
Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not…
It has recently been shown that small quantum subsystems generically equilibrate, in the sense that they spend most of the time close to a fixed equilibrium state. This relies on just two assumptions: that the state is spread over many…
The structure of the initial system-environment state is fundamental to determining the nature and characteristics of the evolution of such an open quantum system. The usual assumption is to consider that the initial system-environment…
Systems whose variable are constrained to be positive allow computationally efficient control design. We generalize these results to linear systems which leave a cone invariant. This is a wider class of systems than positive systems. We…
The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non-Hermitian. Its imaginary part is the time…
We study the behavior of Quantum Darwinism (Zurek, [8]) within the iterative, random unitary operations qubit-model of pure decoherence (Novotny et al, [6]). We conclude that Quantum Darwinism, which describes the quantum mechanical…
Coherent feedback control considers purely quantum controllers in order to overcome disadvantages such as the acquisition of suitable quantum information, quantum error correction, etc. These approaches lack a systematic characterization of…
In this paper, we study linear control systems with positive bounded orbits. We show that the existence of positive bounded orbits imposes strong algebraic and topological constraints on the state space. In fact, a linear control system has…
The destruction of quantum interference, decoherence, and the destruction of entanglement both appear to occur under the same circumstances. To address the connection between these two phenomena, we consider the evolution of arbitrary…
We derive sufficient conditions for infinite-dimensional systems whose entanglement is not completely lost in a finite time during its decoherence by a passive interaction with local vacuum environments. The sufficient conditions allow us…
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.…