352 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
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
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
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
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
Localizable Entanglement
We consider systems of interacting spins and study the entanglement that can
be localized, on average, between two separated spins by performing local
measurements on the remaining spins. This concept of Localizable Entanglement
(LE) leads naturally to notions like entanglement length and entanglement
fluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a
pure quantum state can be lower bounded by connected correlation functions. We
further propose a scheme, based on matrix-product states and the Monte Carlo
method, to efficiently calculate the LE for quantum states of a large number of
spins. The virtues of LE are illustrated for various spin models. In
particular, characteristic features of a quantum phase transition such as a
diverging entanglement length can be observed. We also give examples for pure
quantum states exhibiting a diverging entanglement length but finite
correlation length. We have numerical evidence that the ground state of the
antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum
channel. Furthermore, we apply the numerical method to mixed states and study
the entanglement as a function of temperature.Comment: 19 pages, modified definition of connected string order parameter,
updated reference
Russia's attacks on civilians strengthen Ukrainian resistance
The all-out Russian invasion of Ukraine commencing in February 2022 has been characterized by systematic violence against civilians. Presumably, the commanders of Russian forces believe that, for example, the bombing of residential buildings will force Ukrainians to lay down their arms. We ask whether military attacks against civilians deter or, in contrast, motivate resistance against the attackers. Two- wave probability surveys were collected in Ukraine in March and April 2022 (Ns = 1,081 and 811, respectively). Preregistered analyses indicate that perceptions and experience of military attacks (victimization) did not decrease Ukrainians’ motivations to resist the invading forces. The analyses suggest that victimization positively relates to motivations to join military combat in defense positions. Military attacks against civilians are morally impermissible and prohibited under international humanitarian law. Our results suggest that such attacks are also counterproductive from a military perspective
Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution
We search for translationally invariant states of qubits on a ring that
maximize the nearest neighbor entanglement. This problem was initially studied
by O'Connor and Wootters [Phys. Rev. A {\bf 63}, 052302 (2001)]. We first map
the problem to the search for the ground state of a spin 1/2 Heisenberg XXZ
model. Using the exact Bethe ansatz solution in the limit of an infinite ring,
we prove the correctness of the assumption of O'Connor and Wootters that the
state of maximal entanglement does not have any pair of neighboring spins
``down'' (or, alternatively spins ``up''). For sufficiently small fixed
magnetization, however, the assumption does not hold: we identify the region of
magnetizations for which the states that maximize the nearest neighbor
entanglement necessarily contain pairs of neighboring spins ``down''.Comment: 10 pages, 4 figures; Eq. (45) and Fig. 3 corrected, no qualitative
change in conclusion
On Random Unitary Channels
In this article we provide necessary and sufficient conditions for a
completely positive trace-preserving (CPT) map to be decomposable into a convex
combination of unitary maps. Additionally, we set out to define a proper
distance measure between a given CPT map and the set of random unitary maps,
and methods for calculating it. In this way one could determine whether
non-classical error mechanisms such as spontaneous decay or photon loss
dominate over classical uncertainties, for example in a phase parameter. The
present paper is a step towards achieving this goal.Comment: 11 pages, typeset using RevTeX
Free Banach lattices under convexity conditions
We prove the existence of free objects in certain subcategories of Banach
lattices, including -convex Banach lattices, Banach lattices with upper
-estimates, and AM-spaces. From this we immediately deduce that projectively
universal objects exist in each of these subcategories, extending results of
Leung, Li, Oikhberg and Tursi (\emph{Israel J.\ Math.}~2019). In the
-con\-vex and AM-space cases, we are able to explicitly identify the norms
of the free Banach lattices, and we conclude by investigating the structure of
these norms in connection with nonlinear -summing maps
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