397 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
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
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 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
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 classical and quantum liftings
We analyze the procedure of lifting in classical stochastic and quantum
systems. It enables one to `lift' a state of a system into a state of
`system+reservoir'. This procedure is important both in quantum information
theory and the theory of open systems. We illustrate the general theory of
liftings by a particular class related to so called circulant states.Comment: 25 page
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