27 research outputs found
k-stretchability of entanglement, and the duality of k-separability and k-producibility
The notions of k-separability and k-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this work we reveal a partial duality between them, which is valid also for their correlation counterparts. This duality can be seen from a much wider perspective, when we consider the entanglement and correlation properties which are invariant under the permutations of the subsystems. These properties are labeled by Young diagrams, which we endow with a refinement-like partial order, to build up their classification scheme. This general treatment reveals a new property, which we call k-stretchability, being sensitive in a balanced way to both the maximal size of correlated (or entangled) subsystems and the minimal number of subsystems uncorrelated with (or separable from) one another
The classification of multipartite quantum correlation
In multipartite entanglement theory, the partial separability properties have an elegant, yet complicated structure, which becomes simpler in the case when multipartite correlations are considered. In this work, we elaborate this, by giving necessary and sufficient conditions for the existence and uniqueness of the class of a given class-label, by the use of which we work out the structure of the classification for some important particular cases, namely, for the finest classification, for the classification based on k-partitionability and k-producibility, and for the classification based on the atoms of the correlation properties
A study of separability criteria for mixed three-qubit states
We study the noisy GHZ-W mixture. We demonstrate some necessary but not
sufficient criteria for different classes of separability of these states. It
turns out that the partial transposition criterion of Peres and the criteria of
G\"uhne and Seevinck dealing with matrix elements are the strongest ones for
different separability classes of this 2 parameter state. As a new result we
determine a set of entangled states of positive partial transpose.Comment: 18 pages, 10 figures, PRA styl
The correlation theory of the chemical bond
The quantum mechanical description of the chemical bond is generally given in terms of delocalized bonding orbitals, or, alternatively, in terms of correlations of occupations of localised orbitals. However, in the latter case, multiorbital correlations were treated only in terms of two-orbital correlations, although the structure of multiorbital correlations is far richer; and, in the case of bonds established by more than two electrons, multiorbital correlations represent a more natural point of view. Here, for the first time, we introduce the true multiorbital correlation theory, consisting of a framework for handling the structure of multiorbital correlations, a toolbox of true multiorbital correlation measures, and the formulation of the multiorbital correlation clustering, together with an algorithm for obtaining that. These make it possible to characterise quantitatively, how well a bonding picture describes the chemical system. As proof of concept, we apply the theory for the investigation of the bond structures of several molecules. We show that the non-existence of well-defined multiorbital correlation clustering provides a reason for debated bonding picture
The attractor mechanism as a distillation procedure
In a recent paper it has been shown that for double extremal static
spherically symmetric BPS black hole solutions in the STU model the well-known
process of moduli stabilization at the horizon can be recast in a form of a
distillation procedure of a three-qubit entangled state of GHZ-type. By
studying the full flow in moduli space in this paper we investigate this
distillation procedure in more detail. We introduce a three-qubit state with
amplitudes depending on the conserved charges the warp factor, and the moduli.
We show that for the recently discovered non-BPS solutions it is possible to
see how the distillation procedure unfolds itself as we approach the horizon.
For the non-BPS seed solutions at the asymptotically Minkowski region we are
starting with a three-qubit state having seven nonequal nonvanishing amplitudes
and finally at the horizon we get a GHZ state with merely four nonvanishing
ones with equal magnitudes. The magnitude of the surviving nonvanishing
amplitudes is proportional to the macroscopic black hole entropy. A systematic
study of such attractor states shows that their properties reflect the
structure of the fake superpotential. We also demonstrate that when starting
with the very special values for the moduli corresponding to flat directions
the uniform structure at the horizon deteriorates due to errors generalizing
the usual bit flips acting on the qubits of the attractor states.Comment: 38 pages LaTe
All degree six local unitary invariants of k qudits
We give explicit index-free formulae for all the degree six (and also degree
four and two) algebraically independent local unitary invariant polynomials for
finite dimensional k-partite pure and mixed quantum states. We carry out this
by the use of graph-technical methods, which provides illustrations for this
abstract topic.Comment: 18 pages, 6 figures, extended version. Comments are welcom
Quantum information-based analysis of electron-deficient bonds
Recently, the correlation theory of the chemical bond was developed, which
applies concepts of quantum information theory for the characterization of
chemical bonds, based on the multiorbital correlations within the molecule.
Here for the first time, we extend the use of this mathematical toolbox for the
description of electron-deficient bonds. We start by verifying the theory on
the textbook example of a molecule with three-center two-electron bonds, namely
the diborane(6). We then show that the correlation theory of the chemical bond
is able to properly describe bonding situation in more exotic molecules which
have been synthetized and characterized only recently, in particular the
diborane molecule with four hydrogen atoms [diborane(4)] and neutral zerovalent
s-block beryllium complex, whose surprising stability was attributed to a
strong three-center two-electron bond stretching across the C-Be-C core.
Our approach is of a high importance especially in the light of a constant
chase after novel compounds with extraordinary properties where the bonding is
expected to be unusual