519 research outputs found
On multipartite invariant states II. Orthogonal symmetry
We construct a new class of multipartite states possessing orthogonal
symmetry. This new class defines a convex hull of multipartite states which are
invariant under the action of local unitary operations introduced in our
previous paper "On multipartite invariant states I. Unitary symmetry". We study
basic properties of multipartite symmetric states: separability criteria and
multi-PPT conditions.Comment: 6 pages; slight corrections + new reference
A class of Bell diagonal states and entanglement witnesses
We analyze special class of bipartite states - so called Bell diagonal
states. In particular we provide new examples of bound entangled Bell diagonal
states and construct the class of entanglement witnesses diagonal in the magic
basis.Comment: 17 page
Quantum states with strong positive partial transpose
We construct a large class of bipartite M x N quantum states which defines a
proper subset of states with positive partial transposes (PPT). Any state from
this class is PPT but the positivity of its partial transposition is recognized
with respect to canonical factorization of the original density operator. We
propose to call elements from this class states with strong positive partial
transposes (SPPT). We conjecture that all SPPT states are separable.Comment: 4 page
Geometry of entanglement witnesses parameterized by SO(3) group
We characterize a set of positive maps in matrix algebra of 4x4 complex
matrices. Equivalently, we provide a subset of entanglement witnesses
parameterized 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.Comment: 10 page
Unital Positive Maps and Quantum States
We analyze the structure of the subset of states generated by unital
completely positive quantum maps, A witness that certifies that a state does
not belong to the subset generated by a given map is constructed. We analyse
the representations of positive maps and their relation to quantum
Perron-Frobenius theory.Comment: 14 page
Relations Between Quantum Maps and Quantum States
The relation between completely positive maps and compound states is
investigated in terms of the notion of quantum conditional probability
A class of commutative dynamics of open quantum systems
We analyze a class of dynamics of open quantum systems which is governed by
the dynamical map mutually commuting at different times. Such evolution may be
effectively described via spectral analysis of the corresponding time dependent
generators. We consider both Markovian and non-Markovian cases.Comment: 22 page
On circulant states with positive partial transpose
We construct a large class of quantum "d x d" states which are positive under
partial transposition (so called PPT states). The construction is based on
certain direct sum decomposition of the total Hilbert space displaying
characteristic circular structure - that is way we call them circulant states.
It turns out that partial transposition maps any such decomposition into
another one and hence both original density matrix and its partially transposed
partner share similar cyclic properties. This class contains many well known
examples of PPT states from the literature and gives rise to a huge family of
completely new states.Comment: 15 pages; minor correction
On Reduced Time Evolution for Initially Correlated Pure States
A new method to deal with reduced dynamics of open systems by means of the
Schr\"odinger equation is presented. It allows one to consider the reduced time
evolution for correlated and uncorrelated initial conditions.Comment: accepted in Open Sys. Information Dy
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