Filip Wudarski

We provide a class of entanglement witnesses constructed in terms of mutually unbiased bases (MUBs). This construction reproduces many well-known examples such as the celebrated reduction map and the Choi map together with its generalizations. We illustrate our construction by a detailed analysis of the three-dimensional case: In this case, one obtains a family of entanglement witnesses parametrized by an L-dimensional torus (L=2, 3, 4 being a number of MUBs used in the construction).

The Markovian dynamics of a qubit is investigated in the scheme of random unitary dynamics, where Kraus operators are changed by an extra noise that models imperfect experimental equipment. The behavior of Markovianity is explored in the perturbed scenario. We provide an algorithm for checking completely positive divisibility (Markovianity) of a dynamical map.

It is shown that a convex combination of two non-Markovian evolutions may lead to a Markovian semigroup. This shows that the convex combination of quantum evolutions displaying nontrivial memory effects may result in a perfectly memoryless evolution.

The exchange of "information" between a system and its environment based on the reduced dynamics is investigated. The association of trace distance with information cannot be stated, because of lack of symmetry between leakage from the system and absorbability by the environment. A measure of loss for the reduced dynamics is established, which may be seen as a deviation from exact unitary dynamics.

We analyze the random unitary evolution of a qubit within the memory kernel approach. We provide sufficient conditions which guarantee that the corresponding memory kernel generates physically legitimate quantum evolution. Interestingly, we are able to recover several well-known examples and to generate new classes of nontrivial qubit evolution. Surprisingly, it turns out that a class of quantum evolutions with a memory kernel generated by our approach gives rise to the vanishing of a… Pokaż więcej

We analyze the random unitary evolution of a qubit within the memory kernel approach. We provide sufficient conditions which guarantee that the corresponding memory kernel generates physically legitimate quantum evolution. Interestingly, we are able to recover several well-known examples and to generate new classes of nontrivial qubit evolution. Surprisingly, it turns out that a class of quantum evolutions with a memory kernel generated by our approach gives rise to the vanishing of a non-Markovianity measure based on the distinguishability of quantum states. Pokaż mniej

We analyze the non-Markovianity degree for random unitary evolution of d-level quantum systems. It is shown how the non-Markovianity degree is characterized in terms of local decoherence rates. In particular we derive a sufficient condition for vanishing of the backflow of information and relate this concept to other characteristics of non-Markovianity.

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence… Pokaż więcej

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates. Pokaż mniej

We characterize a set of positive maps in matrix algebra of 4 × 4 complex matrices. Equivalently, we provide a subset of entanglement witnesses in ℂ4⊗ℂ4 parametrized by the rotation group SO(3). Interestingly, these maps/witnesses define two intersecting convex cones in the 3-dimensional parameter space. The existence of two cones is related to the topological structure of the underlying orthogonal group. We perform detailed analysis of the corresponding geometric structure.

We characterize a convex subset of entanglement witnesses for two qutrits. Equivalently, we provide a characterization of the set of positive maps in the matrix algebra of 3 × 3 complex matrices. It turns out that boundary of this set displays elegant representation in terms of SO(2) rotations. We conjecture that maps parametrized by rotations are optimal, i.e. they provide the strongest tool for detecting quantum entanglement. As a byproduct we found a new class of decomposable entanglement… Pokaż więcej

We characterize a convex subset of entanglement witnesses for two qutrits. Equivalently, we provide a characterization of the set of positive maps in the matrix algebra of 3 × 3 complex matrices. It turns out that boundary of this set displays elegant representation in terms of SO(2) rotations. We conjecture that maps parametrized by rotations are optimal, i.e. they provide the strongest tool for detecting quantum entanglement. As a byproduct we found a new class of decomposable entanglement witnesses parametrized by improper rotations from the orthogonal group O(2). Pokaż mniej