165 research outputs found
Binding entanglement channels
We define the binding entanglement channel as the quantum channel through
which quantum information cannot be reliably transmitted, but which can be used
to share bound entanglement. We provide a characterization of such class of
channels. We also show that any bound entangled state can be used to
construction of the map corresponding the binding entanglement channel.Comment: RevTeX, 5 pages, submitted to special issue of J. Mod. Op
Three-by-three bound entanglement with general unextendible product bases
We discuss the subject of Unextendible Product Bases with the orthogonality
condition dropped and we prove that the lowest rank non-separable
positive-partial-transpose states, i.e. states of rank 4 in 3 x 3 systems are
always locally equivalent to a projection onto the orthogonal complement of a
linear subspace spanned by an orthogonal Unextendible Product Basis. The
product vectors in the kernels of the states belong to a non-zero measure
subset of all general Unextendible Product Bases, nevertheless they can always
be locally transformed to the orthogonal form. This fully confirms the
surprising numerical results recently reported by Leinaas et al. Parts of the
paper rely heavily on the use of Bezout's Theorem from algebraic geometry.Comment: 36 page
Duality of cones of positive maps
We study the so-called K-positive linear maps from B(L) into B(H) for finite dimensional Hilbert spaces L and H corresponding to a mapping cone K and give characterizations of the dual cone of the cone of K-positive maps. Applications are given to decomposable maps and their relation to PPT-states
Facial structures for various notions of positivity and applications to the theory of entanglement
In this expository note, we explain facial structures for the convex cones
consisting of positive linear maps, completely positive linear maps,
decomposable positive linear maps between matrix algebras, respectively. These
will be applied to study the notions of entangled edge states with positive
partial transposes and optimality of entanglement witnesses.Comment: An expository note. Section 7 and Section 8 have been enlarge
Classification of bi-qutrit positive partial transpose entangled edge states by their ranks
We construct PPT entangled edge states with maximal ranks, to
complete the classification of PPT entangled edge states by their
types. The ranks of the states and their partial transposes are 8 and 6,
respectively. These examples also disprove claims in the literature.Comment: correct the title to avoid an acronym, correct few text
The canonical phase measurement is pure
We show that the canonical phase measurement is pure in the sense that the
corresponding positive operator valued measure (POVM) is extremal in the convex
set of all POVMs. This means that the canonical phase measurement cannot be
interpreted as a noisy measurement, even if it is not a projection valued
measure.Comment: 4 page
Ola Bratteli and his diagrams
This article discusses the life and work of Professor Ola Bratteli
(1946--2015). Family, fellow students, his advisor, colleagues and coworkers
review aspects of his life and his outstanding mathematical accomplishments.Comment: 18 pages, 15 figure
De Finetti theorem on the CAR algebra
The symmetric states on a quasi local C*-algebra on the infinite set of
indices J are those invariant under the action of the group of the permutations
moving only a finite, but arbitrary, number of elements of J. The celebrated De
Finetti Theorem describes the structure of the symmetric states (i.e.
exchangeable probability measures) in classical probability. In the present
paper we extend De Finetti Theorem to the case of the CAR algebra, that is for
physical systems describing Fermions. Namely, after showing that a symmetric
state is automatically even under the natural action of the parity
automorphism, we prove that the compact convex set of such states is a Choquet
simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of
permutations previously described) are precisely the product states in the
sense of Araki-Moriya. In order to do that, we also prove some ergodic
properties naturally enjoyed by the symmetric states which have a
self--containing interest.Comment: 23 pages, juornal reference: Communications in Mathematical Physics,
to appea
Cloning by positive maps in von Neumann algebras
We investigate cloning in the general operator algebra framework in arbitrary
dimension assuming only positivity instead of strong positivity of the cloning
operation, generalizing thus results obtained so far under that stronger assumption.
The weaker positivity assumption turns out quite natural when considering cloning in
the general C∗-algebra framework
Statistics and Quantum Chaos
We use multi-time correlation functions of quantum systems to construct
random variables with statistical properties that reflect the degree of
complexity of the underlying quantum dynamics.Comment: 12 pages, LateX, no figures, restructured versio
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