204 research outputs found
Exact and Asymptotic Measures of Multipartite Pure State Entanglement
In an effort to simplify the classification of pure entangled states of multi
(m) -partite quantum systems, we study exactly and asymptotically (in n)
reversible transformations among n'th tensor powers of such states (ie n copies
of the state shared among the same m parties) under local quantum operations
and classical communication (LOCC). With regard to exact transformations, we
show that two states whose 1-party entropies agree are either locally-unitarily
(LU) equivalent or else LOCC-incomparable. In particular we show that two
tripartite Greenberger-Horne-Zeilinger (GHZ) states are LOCC-incomparable to
three bipartite Einstein-Podolsky-Rosen (EPR) states symmetrically shared among
the three parties. Asymptotic transformations result in a simpler
classification than exact transformations. We show that m-partite pure states
having an m-way Schmidt decomposition are simply parameterizable, with the
partial entropy across any nontrivial partition representing the number of
standard ``Cat'' states (|0^m>+|1^m>) asymptotically interconvertible to the
state in question. For general m-partite states, partial entropies across
different partitions need not be equal, and since partial entropies are
conserved by asymptotically reversible LOCC operations, a multicomponent
entanglement measure is needed, with each scalar component representing a
different kind of entanglement, not asymptotically interconvertible to the
other kinds. In particular the m=4 Cat state is not isentropic to, and
therefore not asymptotically interconvertible to, any combination of bipartite
and tripartite states shared among the four parties. Thus, although the m=4 cat
state can be prepared from bipartite EPR states, the preparation process is
necessarily irreversible, and remains so even asymptotically.Comment: 13 pages including 3 PostScript figures. v3 has updated references
and discussion, to appear Phys. Rev.
Local symmetry properties of pure 3-qubit states
Entanglement types of pure states of 3 qubits are classified by means of
their stabilisers in the group of local unitary operations. It is shown that
the stabiliser is generically discrete, and that a larger stabiliser indicates
a stationary value for some local invariant. We describe all the exceptional
states with enlarged stabilisers.Comment: 32 pages, 5 encapsulated PostScript files for 3 figures. Published
version, with minor correction
Entangled webs: Tight bound for symmetric sharing of entanglement
Quantum entanglement cannot be unlimitedly shared among arbitrary number of
qubits. Larger the number of entangled pairs in an N-qubit system, smaller the
degree of bi-partite entanglement is. We analyze a system of N qubits in which
an arbitrary pair of particles is entangled. We show that the maximum degree of
entanglement (measured in the concurrence) between any pair of qubits is 2/N.
This tight bound can be achieved when the qubits are prepared in a pure
symmetric (with respect to permutations) state with just one qubit in the basis
state |0> and the others in the basis state |1>.Comment: 4 pages, 1 figur
Evidence for Bound Entangled States with Negative Partial Transpose
We exhibit a two-parameter family of bipartite mixed states , in a
Hilbert space, which are negative under partial transposition
(NPT), but for which we conjecture that no maximally entangled pure states in
can be distilled by local quantum operations and classical
communication (LQ+CC). Evidence for this undistillability is provided by the
result that, for certain states in this family, we cannot extract entanglement
from any arbitrarily large number of copies of using a projection
on . These states are canonical NPT states in the sense that any
bipartite mixed state in any dimension with NPT can be reduced by LQ+CC
operations to an NPT state of the form. We show that the main
question about the distillability of mixed states can be formulated as an open
mathematical question about the properties of composed positive linear maps.Comment: Revtex, 19 pages, 2 eps figures. v2,3: very minor changes, submitted
to Phys. Rev. A. v4: minor typos correcte
Entangled Rings
Consider a ring of N qubits in a translationally invariant quantum state. We
ask to what extent each pair of nearest neighbors can be entangled. Under
certain assumptions about the form of the state, we find a formula for the
maximum possible nearest-neighbor entanglement. We then compare this maximum
with the entanglement achieved by the ground state of an antiferromagnetic ring
consisting of an even number of spin-1/2 particles. We find that, though the
antiferromagnetic ground state does not maximize the nearest-neighbor
entanglement relative to all other states, it does so relative to other states
having zero z-component of spin.Comment: 19 pages, no figures; v2 includes new results; v3 corrects a
numerical error for the case N=
Multipartite pure-state entanglement and the generalized GHZ states
We show that not all 4-party pure states are GHZ reducible (i.e., can be
generated reversibly from a combination of 2-, 3- and 4-party maximally
entangled states by local quantum operations and classical communication
asymptotically) through an example, we also present some properties of the
relative entropy of entanglement for those 3-party pure states that are GHZ
reducible, and then we relate these properties to the additivity of the
relative entropy of entanglement.Comment: 7 pages, Revtex, type error correcte
Classification of multi-qubit mixed states: separability and distillability properties
We give a complete, hierarchic classification for arbitrary multi-qubit mixed
states based on the separability properties of certain partitions. We introduce
a family of N-qubit states to which any arbitrary state can be depolarized.
This family can be viewed as the generalization of Werner states to multi-qubit
systems. We fully classify those states with respect to their separability and
distillability properties. This provides sufficient conditions for
nonseparability and distillability for arbitrary states.Comment: 12 pages, 2 figure
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