228 research outputs found
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
Maximal left ideals of the Banach algebra of bounded operators on a Banach space
We address the following two questions regarding the maximal left ideals of
the Banach algebra of bounded operators acting on an
infinite-dimensional Banach pace :
(Q1) Does always contain a maximal left ideal which is not
finitely generated? (Q2) Is every finitely-generated, maximal left ideal of
necessarily of the form \{T\in\mathscr{B}(E): Tx = 0\} (*) for
some non-zero ?
Since the two-sided ideal of finite-rank operators is not
contained in any of the maximal left ideals given by (*), a positive answer to
the second question would imply a positive answer to the first. Our main
results are: (i) Question (Q1) has a positive answer for most (possibly all)
infinite-dimensional Banach spaces; (ii) Question (Q2) has a positive answer if
and only if no finitely-generated, maximal left ideal of
contains ; (iii) the answer to Question (Q2) is positive for
many, but not all, Banach spaces.Comment: to appear in Studia Mathematic
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.
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
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
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
Approximate quantum data storage and teleportation
In this paper we present an optimal protocol by which an unknown state on a
Hilbert space of dimension can be approximately stored in an
-dimensional quantum system or be approximately teleported via an
-dimensional quantum channel. The fidelity of our procedure is determined
for pure states as well as for mixed states and states which are entangled with
auxiliary quantum systems of varying Hilbert space dimension, and it is
compared with theoretical results for the maximally achievable fidelity.Comment: More detailed discussion of teleportation of entangled and mixed
states. Added reference to work by Banaszek. 8 pages, 1 figur
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