41 research outputs found
Entangled symmetric states of N qubits with all positive partial transpositions
From both theoretical and experimental points of view symmetric states
constitute an important class of multipartite states. Still, entanglement
properties of these states, in particular those with positive partial
transposition (PPT), lack a systematic study. Aiming at filling in this gap, we
have recently affirmatively answered the open question of existence of
four-qubit entangled symmetric states with positive partial transposition and
thoroughly characterized entanglement properties of such states [J. Tura et
al., Phys. Rev. A 85, 060302(R) (2012)] With the present contribution we
continue on characterizing PPT entangled symmetric states. On the one hand, we
present all the results of our previous work in a detailed way. On the other
hand, we generalize them to systems consisting of arbitrary number of qubits.
In particular, we provide criteria for separability of such states formulated
in terms of their ranks. Interestingly, for most of the cases, the symmetric
states are either separable or typically separable. Then, edge states in these
systems are studied, showing in particular that to characterize generic PPT
entangled states with four and five qubits, it is enough to study only those
that assume few (respectively, two and three) specific configurations of ranks.
Finally, we numerically search for extremal PPT entangled states in such
systems consisting of up to 23 qubits. One can clearly notice regularity behind
the ranks of such extremal states, and, in particular, for systems composed of
odd number of qubits we find a single configuration of ranks for which there
are extremal states.Comment: 16 pages, typos corrected, some other improvements, extension of
arXiv:1203.371
Four-qubit entangled symmetric states with positive partial transpositions
We solve the open question of the existence of four-qubit entangled symmetric
states with positive partial transpositions (PPT states). We reach this goal
with two different approaches. First, we propose a
half-analytical-half-numerical method that allows to construct multipartite PPT
entangled symmetric states (PPTESS) from the qubit-qudit PPT entangled states.
Second, we adapt the algorithm allowing to search for extremal elements in the
convex set of bipartite PPT states [J. M. Leinaas, J. Myrheim, and E. Ovrum,
Phys. Rev. A 76, 034304 (2007)] to the multipartite scenario. With its aid we
search for extremal four-qubit PPTESS and show that generically they have ranks
(5,7,8). Finally, we provide an exhaustive characterization of these states
with respect to their separability properties.Comment: 5+4 pages, improved version, title slightly modifie
Separability and distillability in composite quantum systems -a primer-
Quantum mechanics is already 100 years old, but remains alive and full of
challenging open problems. On one hand, the problems encountered at the
frontiers of modern theoretical physics like Quantum Gravity, String Theories,
etc. concern Quantum Theory, and are at the same time related to open problems
of modern mathematics. But even within non-relativistic quantum mechanics
itself there are fundamental unresolved problems that can be formulated in
elementary terms. These problems are also related to challenging open questions
of modern mathematics; linear algebra and functional analysis in particular.
Two of these problems will be discussed in this article: a) the separability
problem, i.e. the question when the state of a composite quantum system does
not contain any quantum correlations or entanglement and b) the distillability
problem, i.e. the question when the state of a composite quantum system can be
transformed to an entangled pure state using local operations (local refers
here to component subsystems of a given system).
Although many results concerning the above mentioned problems have been
obtained (in particular in the last few years in the framework of Quantum
Information Theory), both problems remain until now essentially open. We will
present a primer on the current state of knowledge concerning these problems,
and discuss the relation of these problems to one of the most challenging
questions of linear algebra: the classification and characterization of
positive operator maps.Comment: 11 pages latex, 1 eps figure. Final version, to appear in J. Mod.
Optics, minor typos corrected, references adde
Concurrence classes for an arbitrary multi-qubit state based on positive operator valued measure
In this paper, we propose concurrence classes for an arbitrary multi-qubit
state based on orthogonal complement of a positive operator valued measure, or
POVM in short, on quantum phase. In particular, we construct concurrence for an
arbitrary two-qubit state and concurrence classes for the three- and four-qubit
states. And finally, we construct and class concurrences for
multi-qubit states. The unique structure of our POVM enables us to distinguish
different concurrence classes for multi-qubit states.Comment: 8 page
Concurrence classes for general pure multipartite states
We propose concurrence classes for general pure multipartite states based on
an orthogonal complement of a positive operator valued measure on quantum
phase. In particular, we construct class, , and
class concurrences for general pure -partite states. We give explicit
expressions for and class concurrences for general pure
three-partite states and for , , and class
concurrences for general pure four-partite states.Comment: 14 page
Many body physics from a quantum information perspective
The quantum information approach to many body physics has been very
successful in giving new insight and novel numerical methods. In these lecture
notes we take a vertical view of the subject, starting from general concepts
and at each step delving into applications or consequences of a particular
topic. We first review some general quantum information concepts like
entanglement and entanglement measures, which leads us to entanglement area
laws. We then continue with one of the most famous examples of area-law abiding
states: matrix product states, and tensor product states in general. Of these,
we choose one example (classical superposition states) to introduce recent
developments on a novel quantum many body approach: quantum kinetic Ising
models. We conclude with a brief outlook of the field.Comment: Lectures from the Les Houches School on "Modern theories of
correlated electron systems". Improved version new references adde
Effect of Al3+ ions on antiradical activity of extracts from selected spice plants in model systems
Study on the correlation between chemical structure of selected phenolic compounds, present in raw foods, and their salts and their biodegradability
W ostatnich latach związki polifenolowe zyskują coraz większe zainteresowanie konsumentów i wytwórców żywności. Wyniki badań epidemiologicznych wskazują na prozdrowotne efekty spożywania żywności bogatej w polifenole przede wszystkim ze względu na ich właściwości przeciwutleniające i przeciwrodnikowe. Do tej grupy związków należą hydroksylowe pochodne kwasu benzoesowego. W pracy przedstawiono badania podatności na biodegradację soli wybranych fenolokwasów, różniących się ilością oraz położeniem grup hydroksylowych w cząsteczce oraz toksyczność ostrą w stosunku do wybranych organizmów wskaźnikowych. Stopień biodegradacji oceniano na podstawie redukcji wskaźników zanieczyszczeń tj. RWO i BZT. Określono strukturę analizowanych związków posługując się metodami spektroskopowymi (UV-VIS, FT-IR) oraz teoretycznymi obliczeniami kwantowo-mechanicznymi.Nowadays phenols are compounds of an increasing interest of costumers and food producers. Results of epidemiological researches indicate a health promoting effect of eating foods rich in polyphenols, mainly due to their anti-free radicals and antioxidant properties. Hydroxyl derivatives of benzoic acid belong to this group of compounds. In this paper investigations of biodegradability and the acute toxicity toward indicator organisms of selected phenolic acids differing in the number and location of hydroxyl groups in the molecule and their salts were presented. The degree of biodégradation was determined based on reduction of pollution indicators such as DOC and BOD. The molecular structures of studied compounds were determined by spectroscopic method (UV-VIS, FT-IR) and using quantum-mechanical calculations