67 research outputs found
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
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
On non-Markovian time evolution in open quantum systems
Non-Markovian reduced dynamics of an open system is investigated. In the case
the initial state of the reservoir is the vacuum state, an approximation is
introduced which makes possible to construct a reduced dynamics which is
completely positive
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
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
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