Related papers: When the assignment map is completely positive
We show that complete positivity is not only sufficient but also necessary for the validity of the quantum data-processing inequality. As a consequence, the reduced dynamics of a quantum system are completely positive, even in the presence…
This article introduces PnCP, a MATLAB toolbox for constructing positive maps which are not completely positive. We survey optimization and sum of squares relaxation techniques to find the most numerically efficient methods for this…
Starting form a microscopic system-environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the…
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…
Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot…
Consider the set $\mathcal{S}=\lbrace\rho_{SE}\rbrace$ of possible initial states of the system-environment, steered from a tripartite reference state $\omega_{RSE}$. Buscemi [F. Buscemi, Phys. Rev. Lett. 113, 140502 (2014)] showed that the…
The reduced dynamics of the system $S$, interacting with the environment $E$, is not given by a linear map, in general. However, if it is given by a linear map, then this map is also Hermitian. In order that the reduced dynamics of the…
This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…
We consider a bipartite quantum system $S$ (including parties $A$ and $B$), interacting with an environment $E$ through a localized quantum dynamics $\mathcal{F}_{SE}$ . We call a quantum dynamics $\mathcal{F}_{SE}$ localized if, e.g., the…
A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum…
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…
It is known that the existence of memory effect can revive quantum correlations in open system dynamics. In this regard, the backflow of information from environment to the system can be identified with Complete Positive (CP) indivisibility…
Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we…
We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…
Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement…
We introduce map-dependent quantum characteristic functions constructed from the normalized Choi operator of quantum dynamical maps. We prove a Bochner--Choi positivity theorem establishing that the positive-type condition of the associated…
It is argued that in the description of macroscopic systems inside quantum mechanics the study of the dynamics of selected degrees of freedom slowly varying on a suitable time scale, corresponding to relevant observables for the given…
The relation between completely positive maps and compound states is investigated in terms of the notion of quantum conditional probability.
The Choi representation of completely positive (CP) maps, i.e. quantum channels is often used in the context of quantum information and computation as it is easy to work with. It is a correspondence between CP maps and quantum states also…
We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a…