Coherifying quantum channels

Is it always possible to explain random stochastic transitions between states of a finite-dimensional system as arising from the deterministic quantum evolution of the system? If not, then what is the minimal amount of randomness required by quantum theory to explain a given stochastic process? Here, we address this problem by studying possible coherifications of a quantum channel $\Phi$, i.e., we look for channels $\Phi^{\mathcal{C}}$ that induce the same classical transitions $T$, but are "more coherent". To quantify the coherence of a channel $\Phi$ we measure the coherence of the corresponding Jamio{\l}kowski state $J_{\Phi}$. We show that the classical transition matrix $T$ can be coherified to reversible unitary dynamics if and only if $T$ is unistochastic. Otherwise the Jamio{\l}kowski state $J_\Phi^{\mathcal{C}}$ of the optimally coherified channel is mixed, and the dynamics must necessarily be irreversible. To assess the extent to which an optimal process $\Phi^{\mathcal{C}}$ is indeterministic we find explicit bounds on the entropy and purity of $J_\Phi^{\mathcal{C}}$, and relate the latter to the unitarity of $\Phi^{\mathcal{C}}$. We also find optimal coherifications for several classes of channels, including all one-qubit channels. Finally, we provide a non-optimal coherification procedure that works for an arbitrary channel $\Phi$ and reduces its rank (the minimal number of required Kraus operators) from $d^2$ to $d$.Comment: 20 pages, 8 figures. Published versio

Distinguishing classically indistinguishable states and channels

We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between $M$ quantum states that become identical under a completely decohering map. Similarly, we study distinguishability of $M$ quantum channels that cannot be distinguished when one is restricted to decohered input and output states. The studied problems arise naturally in the presence of a superselection rule, allow one to quantify the amount of information that can be encoded in phase degrees of freedom (coherences), and are related to time-energy uncertainty relation. We present a collection of results on both necessary and sufficient conditions for the existence of $M$ perfectly distinguishable states (channels) that are classically indistinguishable.Comment: 22 pages, 8 figures. Published versio

Quantum discord and its dependence on state purity in two-qubit systems

Celem niniejszej pracy jest zbadanie zależności między rozdźwiękiem kwantowym a czystością stanu.Ponieważ wzory analityczne wyznaczające rozdźwięk są znane tylko dla wąskiej klasy stanów -- tzw. {\it stanówBell-diagonalnych} -- powstał program numerycznie wyznaczający rozdźwięk dla dowolnej zadanej macierzy dwukubitowej. Obliczenia były wykonywane za pomocą pakietu MATLAB.Testowe wyniki programu zostały najpierw porównane ze znanymi wynikami analitycznymi,następnie wykonano obliczenia na losowo wygenerowanym dużym zbiorze stanów dwukubitowych.The aim of this work is to investigate mutual relationships between quantum discord and state purity.Because the analytic formulas defining the quantum discord are known only fora narrow class of states, namely for Bell-diagonal states,an algorithm for numerical determination of the discord for any two-qubitmatrix was designed and implemented. The computations were performed withthe use of MATLAB package. For a number of cases the test numericalresults were compared with the known analytical ones and then numericalcomputations were executed on a large randomly chosen set of two-qubitstates

Man-machine interactions 3

Man-Machine Interaction is an interdisciplinary field of research that covers many aspects of science focused on a human and machine in conjunction.  Basic goal of the study is to improve and invent new ways of communication between users and computers, and many different subjects are involved to reach the long-term research objective of an intuitive, natural and multimodal way of interaction with machines.  The rapid evolution of the methods by which humans interact with computers is observed nowadays and new approaches allow using computing technologies to support people on the daily basis, making computers more usable and receptive to the user's needs.   This monograph is the third edition in the series and presents important ideas, current trends and innovations in  the man-machine interactions area.  The aim of this book is to introduce not only hardware and software interfacing concepts, but also to give insights into the related theoretical background. Reader is provided with a compilation of high-quality original papers covering a wide scope of research topics divided into elven sections,  namely: human-computer interactions, robot control,  embedded and navigation systems, bio data analysis and mining, biomedical signal  processing, image and sound processing, decision support and expert systems, rough and fuzzy systems, pattern recognition, algorithms and optimization, computer networks and mobile technologies and data management systems

4th International Conference on Man–Machine Interactions

This book provides an overview of the current state of research on development and application of methods, algorithms, tools and systems associated with the studies on man-machine interaction. Modern machines and computer systems are designed not only to process information, but also to work in dynamic environment, supporting or even replacing human activities in areas such as business, industry, medicine or military. The interdisciplinary field of research on man-machine interactions focuses on broad range of aspects related to the ways in which human make or use computational artifacts, systems and infrastructure.   This monograph is the fourth edition in the series and presents new concepts concerning analysis, design and evaluation of man-machine systems. The selection of high-quality, original papers covers a wide scope of research topics focused on the main problems and challenges encountered within rapidly evolving new forms of human-machine relationships. The presented material is structured into following sections: human-computer interfaces, robot, control, embedded and navigation systems, bio-data analysis and mining, biomedical signal processing, image and motion data processing, decision support and expert systems, pattern recognition, fuzzy systems, algorithms and optimisation, computer networks and mobile technologies, and data management systems