23,283 research outputs found
Maximally entangled mixed states of two qubits
We consider mixed states of two qubits and show under which global unitary
operations their entanglement is maximized. This leads to a class of states
that is a generalization of the Bell states. Three measures of entanglement are
considered: entanglement of formation, negativity and relative entropy of
entanglement. Surprisingly all states that maximize one measure also maximize
the others. We will give a complete characterization of these generalized Bell
states and prove that these states for fixed eigenvalues are all equivalent
under local unitary transformations. We will furthermore characterize all
nearly entangled states closest to the maximally mixed state and derive a new
lower bound on the volume of separable mixed states
Entanglement, Purity, and Information Entropies in Continuous Variable Systems
Quantum entanglement of pure states of a bipartite system is defined as the
amount of local or marginal ({\em i.e.}referring to the subsystems) entropy.
For mixed states this identification vanishes, since the global loss of
information about the state makes it impossible to distinguish between quantum
and classical correlations. Here we show how the joint knowledge of the global
and marginal degrees of information of a quantum state, quantified by the
purities or in general by information entropies, provides an accurate
characterization of its entanglement. In particular, for Gaussian states of
continuous variable systems, we classify the entanglement of two--mode states
according to their degree of total and partial mixedness, comparing the
different roles played by the purity and the generalized entropies in
quantifying the mixedness and bounding the entanglement. We prove the existence
of strict upper and lower bounds on the entanglement and the existence of
extremally (maximally and minimally) entangled states at fixed global and
marginal degrees of information. This results allow for a powerful, operative
method to measure mixed-state entanglement without the full tomographic
reconstruction of the state. Finally, we briefly discuss the ongoing extension
of our analysis to the quantification of multipartite entanglement in highly
symmetric Gaussian states of arbitrary -mode partitions.Comment: 16 pages, 5 low-res figures, OSID style. Presented at the
International Conference ``Entanglement, Information and Noise'', Krzyzowa,
Poland, June 14--20, 200
Measuring entanglement in condensed matter systems
We show how entanglement may be quantified in spin and cold atom many-body
systems using standard experimental techniques only. The scheme requires no
assumptions on the state in the laboratory and a lower bound to the
entanglement can be read off directly from the scattering cross section of
Neutrons deflected from solid state samples or the time-of-flight distribution
of cold atoms in optical lattices, respectively. This removes a major obstacle
which so far has prevented the direct and quantitative experimental study of
genuine quantum correlations in many-body systems: The need for a full
characterization of the state to quantify the entanglement contained in it.
Instead, the scheme presented here relies solely on global measurements that
are routinely performed and is versatile enough to accommodate systems and
measurements different from the ones we exemplify in this work.Comment: 6 pages, 2 figure
Bipartite and Multipartite Entanglement of Gaussian States
In this chapter we review the characterization of entanglement in Gaussian
states of continuous variable systems. For two-mode Gaussian states, we discuss
how their bipartite entanglement can be accurately quantified in terms of the
global and local amounts of mixedness, and efficiently estimated by direct
measurements of the associated purities. For multimode Gaussian states endowed
with local symmetry with respect to a given bipartition, we show how the
multimode block entanglement can be completely and reversibly localized onto a
single pair of modes by local, unitary operations. We then analyze the
distribution of entanglement among multiple parties in multimode Gaussian
states. We introduce the continuous-variable tangle to quantify entanglement
sharing in Gaussian states and we prove that it satisfies the
Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure,
symmetric three-mode Gaussian states, at variance with their discrete-variable
counterparts, allow a promiscuous sharing of quantum correlations, exhibiting
both maximum tripartite residual entanglement and maximum couplewise
entanglement between any pair of modes. Finally, we investigate the connection
between multipartite entanglement and the optimal fidelity in a
continuous-variable quantum teleportation network. We show how the fidelity can
be maximized in terms of the best preparation of the shared entangled resources
and, viceversa, that this optimal fidelity provides a clearcut operational
interpretation of several measures of bipartite and multipartite entanglement,
including the entanglement of formation, the localizable entanglement, and the
continuous-variable tangle.Comment: 21 pages, 4 figures, WS style. Published as Chapter 1 in the book
"Quantum Information with Continuous Variables of Atoms and Light" (Imperial
College Press, 2007), edited by N. Cerf, G. Leuchs, and E. Polzik. Details of
the book available at http://www.icpress.co.uk/physics/p489.html . For recent
follow-ups see quant-ph/070122
Topological entanglement entropy
We formulate a universal characterization of the many-particle quantum
entanglement in the ground state of a topologically ordered two-dimensional
medium with a mass gap. We consider a disk in the plane, with a smooth boundary
of length L, large compared to the correlation length. In the ground state, by
tracing out all degrees of freedom in the exterior of the disk, we obtain a
marginal density operator \rho for the degrees of freedom in the interior. The
von Neumann entropy S(\rho) of this density operator, a measure of the
entanglement of the interior and exterior variables, has the form S(\rho)=
\alpha L -\gamma + ..., where the ellipsis represents terms that vanish in the
limit L\to\infty. The coefficient \alpha, arising from short wavelength modes
localized near the boundary, is nonuniversal and ultraviolet divergent, but
-\gamma is a universal additive constant characterizing a global feature of the
entanglement in the ground state. Using topological quantum field theory
methods, we derive a formula for \gamma in terms of properties of the
superselection sectors of the medium.Comment: 4 pages, 3 eps figures. v2: reference adde
Quantum coherences, K-way negativities and multipartite entanglement
A characterization of N-partite states, based on K-way (K = 2 to N)
negativities, is proposed. The K-way partial transpose with respect to a
subsystem is defined so as to shift the focus to K-way coherences instead of K
subsystems of the composite system. For an N-partite system the fraction of
K-way negativity, contributing to global negativity, is obtained. The
entanglement measures for a given state are identified as the partial
K-way negativities of the corresponding canonical state.Comment: 09 pages, revtex, new section adde
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