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We identify a set of dynamical maps of open quantum system, and refer to them as "$ \epsilon $-Markovian" maps. It is constituted of maps which, in a higher dimensional system-environment Hilbert space, possibly violate Born approximation…
We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are…
Originated from the superposition principle in quantum mechanics, coherence has been extensively studied as a kind important resource in quantum information processing. We investigate the distinguishability of coherence-breaking channels…
Entropy, and its temporal evolution, play a central role in the foundations of quantum theory and in modern quantum technologies. Here we study, in particular, the relations between the --- in general, non-Markovian --- evolution of an open…
We quantify the consequences of a private key leakage and private randomness generated during quantum key distribution. We provide simple lower bounds on the one-way distillable key after the leakage has been detected. We also show that the…
We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps,…
We consider properties of quantum channels with use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The…
Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary…
We introduce a method to construct non-Markovian variants of completely positive (CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity with the breakdown in CP-divisibility of the map, i.e., appearance of a…
We address the dynamics of quantum correlations for a bipartite continuous-variable quantum system interacting with its fluctuating environment. In particular, we consider two independent quantum oscillators initially prepared in a Gaussian…
Memory effects play a fundamental role in the study of the dynamics of open quantum systems. There exist two conceptually distinct notions of memory discussed for quantum channels in the literature. In quantum information theory quantum…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
Particle-based dynamic occupancy maps were proposed in recent years to model the obstacles in dynamic environments. Current particle-based maps describe the occupancy status in discrete grid form and suffer from the grid size problem,…
In this paper, we study the multiplicative behaviour of quantum channels, mathematically described by trace preserving, completely positive maps on matrix algebras. It turns out that the multiplicative domain of a unital quantum channel has…
Visualizations often encode multivariate data by mapping attributes to distinct visual channels such as color, size, or shape. The effectiveness of these encodings depends on separability--the extent to which channels can be perceived…
To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion,…
Divisible dynamical maps play an important role in characterizing Markovianity on the level of quantum evolution. Divisible maps provide important generalization of Markovian semigroups. Usually one analyzes either completely positive or…
We present a comprehensive and up to date review on the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of quantum Markovian process as a generalization of the classical…
The quantum channels with memory, known as non-Markovian channels, are of crucial importance for a realistic description of a variety of physical systems, and pave ways for new methods of decoherence control by manipulating the properties…
We analyze the connections between the non-Markovianity degree of the most general phase-damping qubit maps and their legitimate mixtures. Using the results for image non-increasing dynamical maps, we formulate the necessary and sufficient…