Related papers: Vanishing quantum discord is necessary and suffici…
We analyze the relation between CP-divisibility and the lack of information backflow for an arbitrary -- not necessarily invertible -- dynamical map. It is well known that CP-divisibility always implies lack of information backflow.…
Quantum discord characterizes "non-classicality" of correlations in quantum mechanics. It has been proposed as the key resource present in certain quantum communication tasks and quantum computational models without containing much…
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…
Let $H$ and $K$ be (finite or infinite dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from ${\mathcal B}(H)$ into ${\mathcal B}(K)$ is given, which particularly gives a…
The requirement of complete positivity is very often regarded as a fundamental consistency condition for the description of open quantum dynamics. We critically examine this requirement and discuss both its physical motivations and its…
Quantum discord is a measure of the quantumness of correlations. After reviewing its different versions and properties, we apply it to the questions of quantum information processing. First we show that changes in discord in the processed…
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…
Recently, a lot of attention has been devoted to finding physically realisable operations that realise as closely as possible certain desired transformations between quantum states, e.g. quantum cloning, teleportation, quantum gates, etc.…
We solve the quantum discord completely as an optimization of certain one variable function for arbitrary two qubit X state. Exact solutions of the quantum discord are obtained for several nontrivial regions of the five parametric space for…
We present a non-demolition quantum information processing task of probing the information of a class of quantum state. In this task, the information is extracted by some unitary evolution with the introduced probing qubit assisted, but the…
Absolutely separable states $\varrho$ remain separable under arbitrary unitary transformations $U \varrho U^{\dag}$. By example of a three qubit system we show that in multipartite scenario neither full separability implies bipartite…
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…
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…
A symmetric matrix $C$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $C=BB^T$. The CP-completion problem is to study whether we can assign values to the missing entries of a partial matrix (i.e.,…
Quantum discord goes beyond entanglement and exists in a wide range of quantum states that may be separable, playing a crucial role in quantum information tasks. In this paper, we firstly proposed a zero-discord criterion for two-qubit…
Quantum simulation is a powerful tool to study the properties of quantum systems. The dynamics of open quantum systems are often described by Completely Positive (CP) maps, for which several quantum simulation schemes exist. We present a…
The relation between completely positive maps and compound states is investigated in terms of the notion of quantum conditional probability.
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…
Open quantum systems have attracted great attention, since inevitable coupling between quantum systems and their environment greatly affects the features of interest of these systems. Quantum discord, is a measure of the total nonclassical…
We argue that notions in quantum theory should have universal properties in the sense of category theory. We consider the completely positive trace preserving (CPTP) maps, the basic notion of quantum channel. Physically, quantum channels…