235 research outputs found
General polygamy inequality of multi-party quantum entanglement
Using entanglement of assistance, we establish a general polygamy inequality
of multi-party entanglement in arbitrary dimensional quantum systems. For
multi-party closed quantum systems, we relate our result with the monogamy of
entanglement to show that the entropy of entanglement is an universal
entanglement measure that bounds both monogamy and polygamy of multi-party
quantum entanglement.Comment: 4 pages, 1 figur
Random bipartite entanglement from W and W-like states
We describe a protocol for distilling maximally entangled bipartite states
between random pairs of parties from those sharing a tripartite W state, and
show that, rather surprisingly, the total distillation rate (the total number
of EPR pairs distilled per W, irrespective of who shares them) may be done at a
higher rate than distillation of bipartite entanglement between specified pairs
of parties. Specifically, the optimal distillation rate for specified
entanglement for the W has been previously shown to be the asymptotic
entanglement of assistance of 0.92 EPR pairs per W, while our protocol can
asymptotically distill 1 EPR pair per W between random pairs of parties, which
we conjecture to be optimal. We thus demonstrate a tradeoff between the overall
asymptotic rate of EPR distillation and the distribution of final EPR pairs
between parties. We further show that by increasing the number of parties in
the protocol that there exist states with fixed lower-bounded distillable
entanglement for random parties but arbitrarily small distillable entanglement
for specified parties.Comment: 5 pages, 1 figure, RevTeX. v2 - upper bound on random distillation is
expressed more generally and corollaries to the bound added. Minor notation
changes. v3 - further notation changes (Ernd now designated Et), discussion
of finite distillation rounds and single-copy bound on Et added. Theorem
added - relative entropy is shown to be an upper bound to Et for all pure
states. Discussion of W formation from EPRs (previously shown in others'
work) removed. Some addition, removal and reordering of reference
Mixed State Entanglement of Assistance and the Generalized Concurrence
We consider the maximum bipartite entanglement that can be distilled from a
single copy of a multipartite mixed entangled state, where we focus mostly on
-dimensional tripartite mixed states. We show that this {\em
assisted entanglement}, when measured in terms of the generalized concurrence
(named G-concurrence) is (tightly) bounded by an entanglement monotone, which
we call the G-concurrence of assistance. The G-concurrence is one of the
possible generalizations of the concurrence to higher dimensions, and for pure
bipartite states it measures the {\em geometric mean} of the Schmidt numbers.
For a large (non-trivial) class of -dimensional mixed states, we are
able to generalize Wootters formula for the concurrence into lower and upper
bounds on the G-concurrence. Moreover, we have found an explicit formula for
the G-concurrence of assistance that generalizes the expression for the
concurrence of assistance for a large class of dimensional
tripartite pure states.Comment: 7 page
Entanglement versus Correlations in Spin Systems
We consider pure quantum states of spins or qubits and study the
average entanglement that can be \emph{localized} between two separated spins
by performing local measurements on the other individual spins. We show that
all classical correlation functions provide lower bounds to this
\emph{localizable entanglement}, which follows from the observation that
classical correlations can always be increased by doing appropriate local
measurements on the other qubits. We analyze the localizable entanglement in
familiar spin systems and illustrate the results on the hand of the Ising spin
model, in which we observe characteristic features for a quantum phase
transition such as a diverging entanglement length.Comment: 4 page
Entanglement of Assistance is not a bipartite measure nor a tripartite monotone
The entanglement of assistance quantifies the entanglement that can be
generated between two parties, Alice and Bob, given assistance from a third
party, Charlie, when the three share a tripartite state and where the
assistance consists of Charlie initially performing a measurement on his share
and communicating the result to Alice and Bob through a one-way classical
channel. We argue that if this quantity is to be considered an operational
measure of entanglement, then it must be understood to be a tripartite rather
than a bipartite measure. We compare it with a distinct tripartite measure that
quantifies the entanglement that can be generated between Alice and Bob when
they are allowed to make use of a two-way classical channel with Charlie. We
show that the latter quantity, which we call the entanglement of collaboration,
can be greater than the entanglement of assistance. This demonstrates that the
entanglement of assistance (considered as a tripartite measure of
entanglement), and its multipartite generalizations such as the localizable
entanglement, are not entanglement monotones, thereby undermining their
operational significance.Comment: 5 pages, revised, title changed, added a discussion explaining why
entanglement of assistance can not be considered as a bipartite measure, to
appear in Phys. Rev.
Deterministic Entanglement of Assistance and Monogamy Constraints
Certain quantum information tasks require entanglement of assistance, namely
a reduction of a tripartite entangled state to a bipartite entangled state via
local measurements. We establish that 'concurrence of assistance' (CoA)
identifies capabilities and limitations to producing pure bipartite entangled
states from pure tripartite entangled states and prove that CoA is an
entanglement monotone for -dimensional pure states.
Moreover, if the CoA for the pure tripartite state is at least as large as the
concurrence of the desired pure bipartite state, then the former may be
transformed to the latter via local operations and classical communication, and
we calculate the maximum probability for this transformation when this
condition is not met.Comment: 5 pages, no figure
Direct versus measurement assisted bipartite entanglement in multi-qubit systems and their dynamical generation in spin systems
We consider multi-qubit systems and relate quantitatively the problems of
generating cluster states with high value of concurrence of assistance, and
that of generating states with maximal bipartite entanglement. We prove an
upper bound for the concurrence of assistance. We consider dynamics of spin-1/2
systems that model qubits, with different couplings and possible presence of
magnetic field to investigate the appearance of the discussed entanglement
properties. We find that states with maximal bipartite entanglement can be
generated by an XY Hamiltonian, and their generation can be controlled by the
initial state of one of the spins. The same Hamiltonian is capable of creating
states with high concurrence of assistance with suitably chosen initial state.
We show that the production of graph states using the Ising Hamiltonian is
controllable via a single-qubit rotation of one spin-1/2 subsystem in the
initial multi-qubit state. We shown that the property of Ising dynamics to
convert a product state basis into a special maximally entangled basis is
temporally enhanced by the application of a suitable magnetic field. Similar
basis transformations are found to be feasible in the case of isotropic XY
couplings with magnetic field.Comment: (14 pages, 7 figures, RevTeX4
Concurrence of assistance and Mermin inequality on three-qubit pure states
We study a relation between the concurrence of assistance and the Mermin
inequality on three-qubit pure states. We find that if a given three-qubit pure
state has the minimal concurrence of assistance greater than 1/2 then the state
violates some Mermin inequality.Comment: 4 pages, 1 figur
Nonergodicity of entanglement and its complementary behavior to magnetization in infinite spin chain
We consider the problem of the validity of a statistical mechanical
description of two-site entanglement in an infinite spin chain described by the
XY model Hamiltonian. We show that the two-site entanglement of the state,
evolved from the initial equilibrium state, after a change of the magnetic
field, does not approach its equilibrium value. This suggests that two-site
entanglement, like (single-site) magnetization, is a nonergodic quantity in
this model. Moreover we show that these two nonergodic quantities behave in a
complementary way.Comment: 4 pages, 2 eps figures, RevTeX4; v2: Published versio
Entanglement in spin chains and lattices with long-range Ising-type interactions
We consider N initially disentangled spins, embedded in a ring or
d-dimensional lattice of arbitrary geometry, which interact via some
long--range Ising--type interaction. We investigate relations between
entanglement properties of the resulting states and the distance dependence of
the interaction in the limit N to infinity. We provide a sufficient condition
when bipartite entanglement between blocks of L neighboring spins and the
remaining system saturates, and determine S_L analytically for special
configurations. We find an unbounded increase of S_L as well as diverging
correlation and entanglement length under certain circumstances. For
arbitrarily large N, we can efficiently calculate all quantities associated
with reduced density operators of up to ten particles.Comment: 4 pages, 2 figures; V2: presentation improved, references adde
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