180 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
Analytic Method Grafpol TM of Synthesing Sequential Control Systems
This paper presents the Grafpol TM method and principles of synthesising sequential control algorithms by this method, as well as examples of applying this method for modelling processes and programming PLC controllers
Medieval multilingualism in Poland:Creating a corpus of Greater Poland court oaths (ROThA)
In this paper we introduce the research plan for the preparation of a searchable electronic repository of the earliest extant legal oaths from medieval Poland drawing on the expertise in historical corpus-building developed for the history of English. The oaths survive in the overwhelmingly Latin land books from the period between 1386 and 1446 for six localities Greater Poland, in which the land courts operated: Poznań, Kościan, Pyzdry, Gniezno, Konin and Kalisz. A diplomatic edition of the oaths was published in five volumes by Polish historical linguists (Kowalewicz & Kuraszkiewicz 1959–1966). The edition is the only comprehensive resource of considerable scope (over 6300 oaths from the years 1386–1446) for the study of the earliest attestations of the Polish language beyond glosses. Recognising some limitations, but most of all its unparalleled coverage of the coexistence of Latin and the vernacular, the ROThA project embarks on transforming the edition into an open up-to-date digital resource. We thus aim to facilitate research into the history of Polish and Latin as well as of the legal system and the related social and linguistic issues of the period
Searching for extremal PPT entangled states
We study extremality in various sets of states that have positive partial
transposes. One of the tools we use for this purpose is the recently formulated
criterion allowing to judge if a given state is extremal in the set of PPT
states. First we investigate qubit--ququart states and show that the only
candidates for extremal PPT entangled states (PPTES) have ranks of the state
and its partial transposition (5,5) or (5,6) (equivalently (6,5)). Then,
examples of extremal states of (5,5) type and the so--called edge states of
type (5,6) are provided. We also make an attempt to explore the set of PPT
states with ranks (5,6). Finally, we discuss what are the possible
configurations of ranks of density matrices and their respective partial
transposition in general three-qubit and four-qubit symmetric states for which
there may exist extremal entangled PPT states. For instance in the first case
we show that the only possibilities are (4,4,4) and (4,4,5).Comment: 12 pages, 2 figures, revised version due to the partial overlap with
results of arXiv:0704.3348, some new results on extremality in multi-qubit
systems added, contribution to the special issue of Optics Communications in
memory of Krzysztof Wodkiewic
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
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