48,347 research outputs found
The Parametric Symmetry and Numbers of the Entangled Class of 2 \times M \times N System
We present in the work two intriguing results in the entanglement
classification of pure and true tripartite entangled state of under stochastic local operation and classical communication. (i) the
internal symmetric properties of the nonlocal parameters in the continuous
entangled class; (ii) the analytic expression for the total numbers of the true
and pure entangled class states. These properties help
people to know more of the nature of the entangled system.Comment: 12 pages, 5 figure
Range criterion and classification of true entanglement in system
We propose a range criterion which is a sufficient and necessary condition
satisfied by two pure states transformable with each other under reversible
stochastic local operations assisted with classical communication. We also
provide a systematic method for seeking all kinds of true entangled states in
the system, and can effectively distinguish them by means
of the range criterion. The efficiency of the criterion and the method is
exhibited by the classification of true entanglement in some types of the
tripartite systems.Comment: 7 papes, no figure, Revtex. This is the published versio
Multipartite entanglement in 2 x 2 x n quantum systems
We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum
system, for example the 4-qubit system distributed over 3 parties, under local
filtering operations. We show that there exist nine essentially different
classes of states, and they give rise to a five-graded partially ordered
structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W
classes of 3 qubits. In particular, all 2 x 2 x n-states can be
deterministically prepared from one maximally entangled state, and some
applications like entanglement swapping are discussed.Comment: 9 pages, 3 eps figure
Classification of multipartite entangled states by multidimensional determinants
We find that multidimensional determinants "hyperdeterminants", related to
entanglement measures (the so-called concurrence or 3-tangle for the 2 or 3
qubits, respectively), are derived from a duality between entangled states and
separable states. By means of the hyperdeterminant and its singularities, the
single copy of multipartite pure entangled states is classified into an onion
structure of every closed subset, similar to that by the local rank in the
bipartite case. This reveals how inequivalent multipartite entangled classes
are partially ordered under local actions. In particular, the generic entangled
class of the maximal dimension, distinguished as the nonzero hyperdeterminant,
does not include the maximally entangled states in Bell's inequalities in
general (e.g., in the qubits), contrary to the widely known
bipartite or 3-qubit cases. It suggests that not only are they never locally
interconvertible with the majority of multipartite entangled states, but they
would have no grounds for the canonical n-partite entangled states. Our
classification is also useful for the mixed states.Comment: revtex4, 10 pages, 4 eps figures with psfrag; v2 title changed, 1
appendix added, to appear in Phys. Rev.
Classification of multipartite entanglement containing infinitely many kinds of states
We give a further investigation of the range criterion and Low-to-High Rank
Generating Mode (LHRGM) introduced in \cite{Chen}, which can be used for the
classification of states under reversible local filtering
operations. By using of these techniques, we entirely classify the family of
states, which actually contains infinitely many kinds of
states. The classifications of true entanglement of
and systems are briefly listed respectively.Comment: 11 pages, revte
Classifying N-qubit Entanglement via Bell's Inequalities
All the states of N qubits can be classified into N-1 entanglement classes
from 2-entangled to N-entangled (fully entangled) states. Each class of
entangled states is characterized by an entanglement index that depends on the
partition of N. The larger the entanglement index of an state, the more
entangled or the less separable is the state in the sense that a larger maximal
violation of Bell's inequality is attainable for this class of state.Comment: 4 pages, 3 figure
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