719 research outputs found
Separable approximations of density matrices of composite quantum systems
We investigate optimal separable approximations (decompositions) of states
rho of bipartite quantum systems A and B of arbitrary dimensions MxN following
the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261
(1998)]. Such approximations allow to represent in an optimal way any density
operator as a sum of a separable state and an entangled state of a certain
form. For two qubit systems (M=N=2) the best separable approximation has a form
of a mixture of a separable state and a projector onto a pure entangled state.
We formulate a necessary condition that the pure state in the best separable
approximation is not maximally entangled. We demonstrate that the weight of the
entangled state in the best separable approximation in arbitrary dimensions
provides a good entanglement measure. We prove in general for arbitrary M and N
that the best separable approximation corresponds to a mixture of a separable
and an entangled state which are both unique. We develop also a theory of
optimal separable approximations for states with positive partial transpose
(PPT states). Such approximations allow to decompose any density operator with
positive partial transpose as a sum of a separable state and an entangled PPT
state. We discuss procedures of constructing such decompositions.Comment: 12 pages, 2 figure
Classification of mixed three-qubit states
We introduce a classification of mixed three-qubit states, in which we define
the classes of separable, biseparable, W- and GHZ-states. These classes are
successively embedded into each other. We show that contrary to pure W-type
states, the mixed W-class is not of measure zero. We construct witness
operators that detect the class of a mixed state. We discuss the conjecture
that all entangled states with positive partial transpose (PPTES) belong to the
W-class. Finally, we present a new family of PPTES "edge" states with maximal
ranks.Comment: 4 pages, 1 figur
Non-Abelian spin singlet states of two-component Bose gases in artificial gauge fields
We study strongly correlated phases of a pseudo-spin-1/2 Bose gas in an
artificial gauge field using the exact diagonalization method. The atoms are
confined in two dimensions and interact via a two-body contact potential. In
Abelian gauge fields, pseudo-spin singlets are favored by pseudo-spin
independent interactions. We find a series of incompressible phases at fillings
\nu=2k/3. By comparison with the non-Abelian spin singlet (NASS) states,
constructed as zero-energy eigenstates of a (k+1)-body contact interaction, we
classify the non-trivial topology of the states. An additional spin-orbit
coupling is shown to switch between NASS-like states and spin-polarized phases
from the Read-Rezayi series.Comment: 4 pages, 3 figure
Nonlocality in many-body quantum systems detected with two-body correlators
Contemporary understanding of correlations in quantum many-body systems and
in quantum phase transitions is based to a large extent on the recent intensive
studies of entanglement in many-body systems. In contrast, much less is known
about the role of quantum nonlocality in these systems, mostly because the
available multipartite Bell inequalities involve high-order correlations among
many particles, which are hard to access theoretically, and even harder
experimentally. Standard, "theorist- and experimentalist-friendly" many-body
observables involve correlations among only few (one, two, rarely three...)
particles. Typically, there is no multipartite Bell inequality for this
scenario based on such low-order correlations. Recently, however, we have
succeeded in constructing multipartite Bell inequalities that involve two- and
one-body correlations only, and showed how they revealed the nonlocality in
many-body systems relevant for nuclear and atomic physics [Science 344, 1256
(2014)]. With the present contribution we continue our work on this problem. On
the one hand, we present a detailed derivation of the above Bell inequalities,
pertaining to permutation symmetry among the involved parties. On the other
hand, we present a couple of new results concerning such Bell inequalities.
First, we characterize their tightness. We then discuss maximal quantum
violations of these inequalities in the general case, and their scaling with
the number of parties. Moreover, we provide new classes of two-body Bell
inequalities which reveal nonlocality of the Dicke states---ground states of
physically relevant and experimentally realizable Hamiltonians. Finally, we
shortly discuss various scenarios for nonlocality detection in mesoscopic
systems of trapped ions or atoms, and by atoms trapped in the vicinity of
designed nanostructures.Comment: 46 pages (25.2 + appendices), 7 figure
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