Non-Markovian quantum dynamics: local versus non-local

We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. These two descriptions are complementary: if one is simple the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point `t_0'. This is the very essence of non-Markovianity. Interestingly, this generator might be highly singular, nevertheless, the corresponding dynamics is perfectly regular. Remarkably, singularities of generator may lead to interesting physical phenomena like revival of coherence or sudden death and revival of entanglement.Comment: 4.5 pages; new examples are adde

On the structure of entanglement witnesses and new class of positive indecomposable maps

We construct a new class of positive indecomposable maps in the algebra of 'd x d' complex matrices. Each map is uniquely characterized by a cyclic bistochastic matrix. This class generalizes a Choi map for d=3. It provides a new reach family of indecomposable entanglement witnesses which define important tool for investigating quantum entanglement.Comment: 18 page

General form of quantum evolution

We propose a complete treatment of a local in time dynamics of open quantum systems. In this approach Markovian evolution turns out to be a special case of a general non-Markovian one. We provide a general representation of the local generator which generalizes well known Lindblad representation for the Markovian dynamics. It shows that the structure of non-Markovian generators is highly intricate and the problem of their classification is still open. Simple examples illustrate our approach.Comment: 4 page

From Markovian semigroup to non-Markovian quantum evolution

We provided a class of legitimate memory kernels leading to completely positive trace preserving dynamical maps. Our construction is based on a simple normalization procedure. Interestingly, when applied to the celebrated Wigner-Weisskopf theory it gives the standard Markovian evolution governed by the local master equation.Comment: 8 page

Multipartite circulant states with positive partial transposes

We construct a large class of multipartite qudit states which are positive under the family of partial transpositions. The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic circular structure and hence generalizes a class of bipartite circulant states proposed recently by the authors. This class contains many well known examples of multipartite quantum states from the literature and gives rise to a huge family of completely new states.Comment: 14 pages; minor change

Rotationally invariant multipartite states

We construct a class of multipartite states possessing rotational SO(3) symmetry -- these are states of K spin-j_A particles and K spin-j_B particles. The construction of symmetric states follows our two recent papers devoted to unitary and orthogonal multipartite symmetry. We study basic properties of multipartite SO(3) symmetric states: separability criteria and multi-PPT conditions.Comment: 18 pages; new reference

On partially entanglement breaking channels

Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement. These classes generalize the well known class of entanglement breaking channels.Comment: 9 page

A new class of states with positive partial transposition

We construct a new class of PPT states for bipartite "d x d" systems. This class is invariant under the maximal commutative subgroup of U(d) and contains as special cases almost all known examples of PPT states. Theses states may be used to test the atomic property of positive maps which are crucial in studying quantum entanglement.Comment: 4.5 page

Antibody-Mediated Rejection: An Evolving Entity in Heart Transplantation

Antibody-mediated rejection (AMR) is gaining increasing recognition as a major complication after heart transplantation, posing a significant risk for allograft failure, cardiac allograft vasculopathy, and poor survival. AMR results from activation of the humoral immune arm and the production of donor-specific antibodies (DSA) that bind to the cardiac allograft causing myocardial injury predominantly through complement activation. The diagnosis of AMR has evolved from a clinical diagnosis involving allograft dysfunction and the presence of DSA to a primarily pathologic diagnosis based on histopathology and immunopathology. Treatment for AMR is multifaceted, targeting inhibition of the humoral immune system at different levels with emerging agents including proteasome and complement inhibitors showing particular promise. While there have been significant advances in our current understanding of the pathogenesis, diagnosis, and treatment of AMR, further research is required to determine optimal diagnostic tools, therapeutic agents, and timing of treatment

Tankyrase represses autoinflammation through the attenuation of TLR2 signaling

Dysregulation of Toll-like receptor (TLR) signaling contributes to the pathogenesis of autoimmune diseases. Here, we provide genetic evidence that tankyrase, a member of the poly(ADP-ribose) polymerase (PARP) family, negatively regulates TLR2 signaling. We show that mice lacking tankyrase in myeloid cells developed severe systemic inflammation with high serum inflammatory cytokine levels. We provide mechanistic evidence that tankyrase deficiency resulted in tyrosine phosphorylation and activation of TLR2 and show that phosphorylation of tyrosine 647 within the TIR domain by SRC and SYK kinases was critical for TLR2 stabilization and signaling. Last, we show that the elevated cytokine production and inflammation observed in mice lacking tankyrase in myeloid cells were dependent on the adaptor protein 3BP2, which is required for SRC and SYK activation. These data demonstrate that tankyrase provides a checkpoint on the TLR-mediated innate immune response